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Issued April 24, 1913. 

U. S. DEPARTMENT OF AGRICULTURE. 

BUREAU OF PLANT INDUSTRY— BULLETIN NO. 269. 

B. T. GALLOWAY, Chief of Bureau. 



EXPERIMENTS IN WHEAT BREEDING 

EXPERIMENTAL ERROR IN THE NURSERY AND 
VARIATION IN NITROGEN AND YIELD. 



BY 



E. G. MONTGOMERY, 

Experimental Agronomist of the Nebraska Agricultural Experiment Station 

and Collaborator of the Office of Cereal Investigations, 

Bureau of Plant Industry. 




WASHINGTON: 

GOVERNMENT PRINTING OFFICE. 

1913. 



, ^ 






BUREAU OF PLANT INDUSTRY. 



Chief of Bureau, Beverly T. Galloway. 
Assistant Chief of Bureau, William A. Tayxor. 
Editor, J. E. Rockwell. 
Chief Clerk, James E. Jones. 



Cereal Investigations. 

scientific staff. 

Carleton R. Ball, A ding Cerealist in Charge. 
Charles E. Chambliss, H. B. Derr, H. V. Harlan, and C. W. Warburton, Agronomists. 

E. L. Adams, Assistant Agronomist. 
Clyde E. Leighty, Expert. 

Cecil Salmon, Physiologist. 

John F. Ross, Farm Superintendent. 

A. A. Potter, Assistant Pathologist. 

L. C. Aicher, P. V. Cardon, Manley Champlin, J. A. Clark, N. C. Donaldson, J. Mitchell Jenkins, E. M. 

Johnston, Jenkin W. Jones, F. A. Kiene, jr., Clyde McKee, J. D. Morrison, B. E. Rothgeb, T. R. Stanton, 

and L. Wermelskirchen, Scientific Assistants. 

F. R. Babcock, Assistant. 

L. R. Breithaupt, L. C. Burnett, and H. H. Love, Agents. 
D. E. Stephens, Executive Assistant. i 



D, OF D, 
*PK 3J 1913 



LETTER OF TRANSMITTAL 



U. S. Department of Agriculture, 

Bureau of Plant Industry, 

Office of the Chief, 
Washington, D. C, October 16, 1912. 
Sir: I have the honor to transmit herewith and to recommend for 
publication as Bulletin No. 269 of the series of this Bureau the 
accompanying paper entitled "Experiments in Wheat Breeding: 
Experimental Error in the Nursery and Variation in Nitrogen and 
Yield," by Prof. E. G. Montgomery. This paper contains the results 
of special experiments in wheat breeding conducted by the Nebraska 
Agricultural Experiment Station in cooperation with the Office of 
Cereal Investigations of this Bureau, during the years 1905 to 1910, 
inclusive. In part, the work is a continuation of that recorded in 
Bureau of Plant Industry Bulletin No. 78, by Dr. T. L. Lyon, under 
whose direction the experiments were conducted from 1902 to 1906, 
inclusive. From 1907 to 1910, inclusive, the work was under the 
charge of Prof. Montgomery, experimental agronomist of the Ne- 
braska experiment station, who has since become professor of farm 
crops in the College of Agriculture at Cornell University. 

The paper is concerned chiefly with the nature and extent of 
experimental error in the wheat nursery in connection with breeding 
experiments in the inheritance of nitrogen content and yield in wheat 
plants. The standardization of agronomic experiments has been 
receiving much attention in recent years and is regarded as of fun- 
damental importance in agronomic research. The results contained 
in this paper are presented as a contribution to this subject as well as 
to the improvement of wheat. 

Respectfully, B. T. Galloway, 

Chief of Bureau. 
Hon. James Wilson, 

Secretary of Agriculture. 

269 



CONTENTS. 



Page. 

I. Experimental error in the nursery and variation in nitrogen content 9 

Introduction , 9 

Relation of yield of grain to nitrogen content 19 

Reducing the experimental error 22 

Replication of single plants 22 

Replication of 2-foot rows 24 

Replication of 16- foot rows ■ 25 

The small-block test 27 

Increasing the size of plat 29 

The limit of experimental error 30 

Summary 31 

II. Experimental error in the nursery and variation in yield 33 

Introduction 33 

Variation in yield from check rows 33 

Variation in yield from repeated rows 34 

Variation in yield from small blocks 37 

Effect of repetition in reducing error 38 

Relation of size of plat to variation 39 

Constancy of variation on the same plats 41 

Variation in yields from centgener plats 41 

Alternating check rows as a means of obtaining comparative yields. . . 42 

Effect of increasing length of row 42 

Influence of rate of planting on yield 45 

Effect of competition between adjacent rows 47 

Variation in pure strains and relation of data in centgener nursery 

and in field plats 48 

Isolation of pure strains 48 

Percentage of nitrogen 52 

Strength of straw : 52 

Yield per plant 53 

Yield per centgener 53 

Size of kernel 53 

Quality of kernel 53 

Superiority of strain 54 

Comparison of rows, centgeners, blocks, and field plats 55 

Cost of planting and harvesting centgeners, rows, and blocks 56 

Use of check plats 58 

Error in check plats 59 

Other precautions against error 60 

Accidental injury to plats 60 

Unequal drainage 60 

Summary 60 

269 

5 



TABLES. 

Page. 
Table I. Results of a study of transmission of nitrogen content in wheat ker- 
nels in 1902 and 190:5 10 

II. Nitrogen content of 57 wheat plants in 1903 and of their progeny in 

1904 and 1905 11 

III. Data from six wheat plants, showing irregular variation in yield 

and in nitrogen content of grain 12 

IV. Nitrogen content and yield of grain from families Nos. 42 and 48, 

from ] 902 to 1905, inclusive 1 G 

V. Nitrogen content of 29 centgeners and corresponding rows from 

family No. 831 in 1908 19 

VI. Nitrogen content and yield of grain from 180 wheat plants, arranged 

in inverse order of percentage of nitrogen, in groups of 10 20 

VII. Nitrogen content of 90 plants of Turkey wheat from 1 centgener 
and of 840 plants variously combined into groups to show devia- 
tion from mean 23 

VIII. Nitrogen content of 110 2-foot sections of drill row of Turkey wheat. . 24 

IX. Nitrogen content of 100 16-foot rows of Turkey wheat 25 

X. Summary showing degree of error due to variation in environment, 

according to several methods of comparison 26 

XI. Nitrogen content of Turkey wheat grown in 224 block plats in 1909 

and 1910 27 

XII. Yield of 47 14-foot check plats of Turkey wheat in 1909 34 

XIII. Yield of thrashed grain from 100 rows of Kherson oats 35 

XLV. Yield of grain from 500 16-foot rows of Turkey wheat, systematically 

repeated in various ways to show experimental error 36 

XV. Yield of Turkey wheat grown in 224 block plats in 1909 and 1910. . . 39 
XVI. Yield, in grams, of Turkey wheat grown during the season of 1910 in 

500 rows, each 16 feet in length 43 

XVII. Summary showing coefficients of variability under various systems 

of arranging block plats and row plats 45 

XVIII. Results of rate-of-seeding test on 100 16-foot rows of Red Rustproof 

oats .• 46 

XIX. Results of rate-of-seeding test on 60 block plats of Kherson oats 47 

XX. Relations of certain characters of 24 strains of Turkey wheat grown 

in nursery and in field and tested during 4-year periods 48 

XXI. Yields of grain from 11 varieties of oats grown in field plats, cent- 
geners, rows, and blocks 56 

XXII. Comparative number of plats of different types that can be planted 

or harvested in 10 hours 57 

269 
6 



ILLUSTRATIONS. 



PLATES. 

Page. 
Plate I. Fig. 1. — Head-to-row nursery, in which 25 grains from a single head 
are planted in a row 20 inches long. Fig. 2. — Row-plat nursery, 
in which the rows are 16 feet in length with a 4-foot alley between 

beds, thus making the beds 20 feet in width 42 

II. Fig. 1. — Increase plats of one-thirtieth acre each. Fig. 2. — Increase 

plats harvested and ready to thrash 42 

III. Fig. 1. — Type of road grader or drag used in grading a nursery into 

beds. Fig. 2. — Grains of Turkey wheat, showing variation in 
appearance 52 

IV. Fig. 1. — Representative kernels from four strains of Turkey wheat, 

selected to show variation in appearance. Fig. 2. — Representa^ 
tive kernels from four strains of Turkey wheat, selected from a 
series of 80 strains to show variation in quality 52 

TEXT FIGURES. 

Fig. 1. Diagram showing the transmission of nitrogen content in 57 wheat 

plants of 1903 to progeny in 1904 and 1905 10 

2. Centgener nursery, Nebraska Agricultural Experiment Station 12 

3. Wheat centgener just after growth has started in spring, showing about 

40 per cent of the plants winterkilled 13 

4. Wheat centgener of 100 plants, showing variations in yield of grain 

and of nitrogen in 1907 14 

5. Diagram of a portion of the wheat nursery in 1907, showing variations 

in nitrogen content in centgeners and families 15 

6. Diagram of 10 centgeners and 10 corresponding rows, showing varia- 

tions in nitrogen content for individual plants, for each centgener, 

for each corresponding row, and also for their parents 18 

7. Diagram of plat of Turkey wheat containing 224 blocks, showing the 

location of each block and variations in the percentage of nitrogen in 

the grain ' 22 

8. Diagrams of plats of Turkey wheat, showing the arrangement of 224 

blocks when combined in groups of adjacent blocks, with average 
nitrogen content for each group 22 

9. Diagram showing the method of selection for nitrogen content when 

the experimental error is known 31 

10. Diagram of plats of Turkey wheat, showing the arrangement of 224 

blocks and the yield of grain for each block 37 

11. Diagrams of plats of Turkey wheat, showing the arrangement of 224 

blocks when combined in groups of adjacent blocks, with the aver- 
age yield for each group 38 

269 

7 



ILLUSTRATIONS. 

Page. 

12. Diagrams showing Turkey wheat grown in 224 blocks, combined in 

four groups of 56 adjacent blocks to show variations in yield and 
nitrogen content 41 

13. Field plats of pure strains and check plats of original seed of Turkey 

wheat, 1910 50 

14. Wheat nursery plats, showing variations in winterkilling 50 

15. Field plats, showing variations in winterkilling between two pure 

strains of Turkey wheat 51 

16. Increase rows of Turkey wheat, showing variations in the time of head- 

ing in different strains 52 

17. Field plats of Turkey wheat, showing variations in stiffness of straw 

in two strains 53 

18. Cereal laboratory, showing the method of taking notes on quality 54 

19. Block nursery, showing blocks 4.2 by 16 feet in size . .' 55 

20. Five-row nursery drill used for planting row plats and block plats 57 

21. Row plats at harvest time 58 

22. Diagram showing the method of selection for yield when the experi- 

mental error is known 59 

269 



B. P. I.— 785. 



EXPERIMENTS IN WHEAT BREEDING: EXPERI- 
MENTAL ERROR IN THE NURSERY AND VARIA- 
TION IN NITROGEN AND YIELD. 



I -EXPERIMENTAL ERROR IN THE NURSERY AND VARIATION 
IN NITROGEN CONTENT. 



INTRODUCTION. 

The investigation of the variation of plants of winter wheat in 
relative nitrogen content when grown under field or nursery condi- 
tions was begun by Dr. T. L. Lyon, formerly agronomist of the 
Nebraska Agricultural Experiment Station, in collaboration with the 
Bureau of Plant Industry of the United States Department of Agri- 
culture. His results were published as a bulletin of that bureau. 1 
Since 1907 the investigation has been continued by the writer and 
his assistants. 2 

One of the striking features of the data obtained by Dr. Lyon was 
the variation in nitrogen content of the kernels from different plants 
of wheat grown under apparently similar conditions. For example, 
800 spikes of Turkey wheat were selected and half of each spike 
analyzed for proteid nitrogen, the lowest having only 1.12 per cent 
while the highest contained 4.95 per cent. 

In 1903, 288 plants which were the progeny from 119 of the spikes 
analyzing above 3 per cent proteid nitrogen in 1902 were analyzed 
and found to vary from 1.20 per cent to 5.85 per cent in nitrogen 
content. In most of the families only a single plant was selected 
for analysis, but in the remainder two to six plants were selected. 
Even where all the plants were grown from a single parent the varia- 
tion was quite as great. 

1 Lyon, T. L. Improving the Quality of Wheat. Bulletin 78, Bureau of Plant Industry. 1905. 

2 The writer wishes to acknowledge with thanks the assistance of a number of men who have contrib- 
uted to the production of these data. Dr. T. L. Lyon, now of Cornell University, planted the first wheat 
nursery in 1902 and conducted the work until 1906, being assisted by Prof. Alvin Keyser, now of the Colo- 
rado Agricultural Experiment Station. They left an excellent set of records, from which data previous 
to 1906 have been prepared (Table II). Mr. L. L. Zook, now of the Bureau of Plant Industry, assisted 
with the work in 1907 and 1908, as did Mr. Erwin Hopt in 1908 and 1909. Prof. T. A. Kiesselbach had 
charge of the records during the seasons of 1909 and 1910 and has prepared much of the tabular matter for 
publication. The chemical analysis has been under the direction of Dr. F. J. Alway, who devised a rapid 
method especially for this work. 

69826°— bul. 269—13 2 . 

9 



10 



EXPERIMENTS IN WHEAT BREEDING. 



Dr. Lyon noted this variation, as follows: 

For instance, the plants numbered 21205 to 21212, all of which come from the same 
parent, vary from 2.16 to 5.23 per cent in proteid nitrogen content, while plants 
69805 and 69806 vary from 5.82 to 1.66 per cent in this constituent. 1 

In addition to the 119 "highs" preserved in 1903, progeny were 
analyzed also from 20 "mediums" and "lows." When these data 
were summarized it seemed that there had been some tendency to 
transmit the character, as shown in Table I. 

Table I.— Results of a study of transmission of nitrogen content in wheat kernels in 

1902 and 190 J 2 



Llange in percentage of proteid nitrogen. 



Number 
of analy- 
ses aver- 



Pro teid 

nitrogen in 
kernels. 



lto3 

3 and over. 



Per cent. 
20 j L85 

119 3.39 



Number 

of analy- 
ses ave'r- 



70 
288 



Proteid 

nitrogen in 

kernels. 



Per cent. 
2.59 
2.92 




Fig. 1. — Diagram showing the transmission of 
nitrogen content in 57 wheat plants of 1903 to 
progeny in 1904 and 1905. The vertical lines 
represent successive years. The horizontal 
lines represent the percentage of nitrogen 
found, and the figures in parentheses show the 
number of plants in each group analyzed for 
nitrogen content in 1903. 

269 



Summaries of the results obtained 
in 1904 and 1905 show very little 
tendency to transmit this charac- 
ter. 

In 1906, after four years of selec- 
tion of extremely high fluctuates, 
and later, after two more years of 
selection, by taking a composite 
sample of all the progeny of a plant 
it was found that no gain had been 
made in the nitrogen content of the 
crop. 

In Table II is a summary of data 
obtained in the years 1903 to 1905 
from 57 of the original plants. Fig- 
ure 1 is a graphic presentation of 
the same data, in which the hori- 
zontal lines represent the percent- 
age of nitrogen, the vertical lines 
represent successive years, and the 
figures in parentheses show the num- 
bers of plants in each of the seven 
groups analyzed for nitrogen content 
in 1903. 



i Lyon, T. L. 
2 Lyon, T. L. 



Op. cit., p. 99. 

Op. cit., table 26, p. 98. 



EXPERIMENTAL ERROR AND VARIATION IN NITROGEN. 



11 



Table II. — Nitrogen content of 57 wheat plants in 190,3 and of their progeny in 1904 
and 1905, arranged in groups according to the percentage of nitrogen. 



Record of 57 plants 
1903. 


harvested in 


Record of progeny plants in 1904. 


Record of progeny plants in 1905. 




Kernels per 


Nitrogen in 




Kernels per 


Nitrogen in 




Kernels per 


Nitrogen in 




plant. 


kernels. 


w 


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kernels. 


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11.26 


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1,165 


21.44 


2.69 


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5.87 


3.27 


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19.49 


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3. 68 


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2.65 


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22.02 


2.80 


.6153 


5 


274 


5.68 


5.13 


.2773 


25. . . . 


716 


10. 56 


2.59 


.2710 


81.... 


1,1S3 


20.12 


2.64 


.5317 



It is difficult to explain why such great variations exist when there 
seems to be little or no tendency to transmit them. It seems ap- 
parent that the variations must be due to differences in environment. 
Since the ordinary factors of environment, as sunlight, warmth, 
moisture, and apparent fertility of the soil, are constant for all 
plants under our nursery conditions, we must conclude that there 
are factors profoundly influencing the growth of plants beyond the 
ordinary range of observation. 

Figure 2 shows the general appearance of the centgener nursery, 
each centgener containing 100 plants 6 inches apart each way. 
Figure 3 shows a single centgener just after growth has started in 
the spring, about 40 per cent of the plants having winterkilled. The 
great variation in the size of the remaining plants is probably due to 
the effect of environment and is not hereditary. This environmental 
variation is usually noted even in centgeners where most plants have 
survived and is often interpreted as indicating real hereditary 
differences. 

A number of interesting problems are suggested. Why should one 
plant, growing under practically the same environment as another, 
collect from the soil two or three times as much nitrogen ? Or why 
should two plants yielding different quantities of grain collect the 
same quantities of nitrogen ? Table III illustrates these variations. 

269 



12 



EXPERIMENTS IN WHEAT BREEDING. 



Table III. — Data from six wheat plants, showing irregular variation in yield and in 

nitrogen content of grain. 



Plant 
No. 


Kernels. 


Nitrogen in kernels. 


Plant 
No. 


Kernels. 


Nitrogen in kernels. 


Number. 


Weight. 


Per cent. 


Total 
weight. 


Number. 


Weight. 


Per cent. 


Total 
weight. 


21107 

21108 

21109 


1,058 

1,030 

927 


Grams. 
22. 879 
16. 679 
16. 026 


2.45 
2.59 
1.74 


Grams. 

0. 5605 

. 4324 

.2789 


23905 
23907 
24005 


776 
1,167 
1,495 


Grams. 
18.507 
23. 01S 
30.064 


3.57 
2.86 
2.19 


Grams. 
0.6607 
.6583 
.6584 



The three plants, Xos. 21107 to 21109, are from the same mother 
growing in a single centgener, probably less than 2 feet apart, yet 
the actual grams of nitrogen gathered differ more than 100 per 




Fig. 2. — Centgener nursery, Nebraska Agricultural Experiment Station. Each centgener contains 

100 plants. 

cent. This difference is not inherited, as these plants rarely trans- 
mit this quality. It therefore seems hard to explain on a difference 
in the root development or in the functioning parts of the plant. As 
plants growing only 6 inches apart commonly exhibit such differ- 
ences, it can not be ascribed to a difference in soil solution. Differ- 
ence in vigor of growth is not a satisfactory explanation, as plants 
Xos. 23905, 23907, and 24005 illustrate. These three plants under 
uniform conditions yielded different quantities of grain, yet the 
heaviest yielder produced no more nitrogen than the lowest. Such 
differences are not only common among plants from the same cent- 
gener, but quite marked variations are also noted between cent- 
geners from the same mother plant. 

269 



EXPERIMENTAL ERROR AND VARIATION IN NITROGEN. 



13 



Some of the results obtained from the study of this problem are shown 
in figures 4 and 5. Figure 4 is a plat of a single centgener (1907), 
with the plants 6 inches apart each way, making the entire area 5 
feet square. All plants in this centgener are from the same parent. 
Each square represents a plant. Where no figures occur the plant 
was missing. The upper number shows the percentage of nitrogen, 
the central number represents the kernels borne by the plant, and 
the lower number the weight in grams of the good kernels. Each 
plant was harvested separately, the kernels counted and weighed, 
and the percentage of nitrogen determined. Two wave lines indicate 
plants analyzing above 3 per cent nitrogen and one wave line those 




Fig. 3.— Wheat centgener just after growth has started in spring, showing about 40 per cent of the 
plants winterkilled. Note the great variation in size of the remaining plants. 

analyzing between 2.8 and 3 per cent. A tendency to group is noted. 
Those containing between 2.56 and 2.80 per cent are not marked. 
One straight line indicates plants with between 2.55 and 2.40 per 
cent of nitrogen; two straight lines, less than 2.40 per cent. 

Figure 5 shows a section of the wheat nursery in 1907. The small 
squares represent centgeners 5 feet square and the heavy lines out- 
line family groups; that is, all the plants and centgeners within a 
heavy line came from the same original plant. The percentage of 
nitrogen was obtained by taking a composite sample from all plants 
on the centgener. Variation is quite marked, although there is 
some tendency for certain families to run high or low; as, for example, 
family 339. 

269 



14 



EXPERIMENTS IN WHEAT BREEDING. 



An illustration of the irregularities in number and weight of ker- 
nels, in percentage of nitrogen, and in total yield of nitrogen per 
plant is afforded in Table IV, pedigree records of two families. The 
wide variations were supposed at first to represent natural fluctua- 
tions which would be in some degree transmitted, but the selection of 
these high fluctuations has had no apparent effect in modifying the 




g.gi 

247 
6.80 



2.32 

299 
8.8G 



2.52 



SO/ 

13.4- 



252 
36/ 
IO. o 




2.55 

446 

15.7 



2.60 
S07 

13.8 



2.60 
40/ 



2.6Q 
347 

e.a 



2.63 
£49 

15.0 



2.52 
4// 

1 1. a 



2.72 
6/3 

12.5 



2.53 



409 
9.8 



2.5Q 

4/7 

10. 1 



2.56 
227 

5.3 



2.75 
S43 

14.3 



2.56 
60/ 
17.5 



2.23 
4/0 
I I.O 



2.56 
284 

a.o 



2.63 
390 

9.4- 



2.66 

370 

9.3 



466 
10.4- 



2.45 

322 

8.9 



275 

406 

9.7 



2.69 

392 

9.5 



J^J6. 

~2^6 

3.8 



3. IO 

362 
7.6 



2.8 



2.42 
8.5 



3. OS 



3.20 



9.5 



2.71 

467 

5.3 





2.60 
379 
7.4- 




2.66 
470 

II. I 



2.76 



277 
362 

4.8 




10.8 



2.52 



66/ 

16.8 






2.58 
^■7(? 

14.4 



2.60 
S/O 

12.1 



2.58 
8.1 



3.M 
7.5 



Fig. 4. — Wheat centgener of 100 plants, showing variations in yield of grain and of nitrogen in 1907. Upper 
figures, percentage of nitrogen content; middle figures, number of kernels produced; lower figures, weight 
of good kernels in grams. The various underscorings of the upper figures indicate five groups having 
successively higher nitrogen content as follows: (1) Figures underscored with two straight lines lie between 
2.15 and 2.40 per cent; (2) those underscored with one straight line lie between 2.41 and 2.55 per cent; 
(3) those not underscored lie between 2.56 and 2.59 per cent; (4) those underscored with one wave line 
lie between 2. SO and 3 per cent; (5) those underscored with two wave lines lie above 3 per cent. 

nitrogen content of plants in a family, as there always seemed to be 
a mean content for each family, to which the types returned. 

As examples of variation, note that No. 35809 in family 42 has a 
low yield of nitrogen, yet the yield of nitrogen found in its progeny 
is practically equal to that of other members of the family. In 
family 48 (Table IV) note that in 1903 the three plants selected 
analyzed 3.82, 4.43, and 5.48 per cent of nitrogen, respectively, 

2G9 



EXPERIMENTAL ERROR AND VARIATION IN NITROGEN. 



15 



while the family as a whole contained 3.53 per cent. The progeny 
of these plants returned to normal in percentage and total yield of 
nitrogen, except No. 21909, in which the yield of grain was above 
the average. Just why these wide fluctuations occur when every 
precaution is taken to grow the plants under uniform conditions is 
not very apparent. 

In 1908 a more thorough investigation of this point was made. 
Twenty-nine plants from the 1907 crop were all selected from a single 
centgener, and therefore all came from a single plant in 1906. From 
each of these 29 plants a centgener was planted, and also a row 14 
feet long. The 29 centgeners were planted side by side, also the 29 
rows. At harvest time all the plants in each of the 10 adjacent 



2. 35 
313 


314 


2 65 

314- 


2.93 
32 8 


3 04 

3 as 


2.89 

SSI 


2.73 
3SI 


2 56 
38S 


259 
335 


2.89 
405 


2.77 
405 


a.62 

417 


2.55 
417 


277 
S22 


2.71 
522 


2.55 
556 


289 

556 


2.43 
3 


277 
3 


2.46 
313 


2.60 
3I4 


2 72 

3)4 


3O0 

328 


2. 45 
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Fig. 5.— Diagram of a portion of the wheat nursery in 1907, showing variations in nitrogen content in cent- 
geners and families. Each square represents a single centgener, and each area within heavy lines shows 
the centgeners belonging to a single family. The upper figures represent the percentage of nitrogen; 
the lower figures are the family numbers. 

centgeners were harvested in order and analyzed. The 10 dupli- 
cate rows were grown in a manner similar to field conditions; that is, 
sown at the rate of 5 pecks to the acre and the rows 8 inches apart. 
The plan was to see whether the same sort of variation would be 
found among plants under field conditions. To secure a uniform 
sample from the rows, 7 plants were harvested from each foot of 
row, 98 plants being harvested and analyzed from each row. In the 
centgeners the results were similar to those obtained in 1907. The 
plants in the rows, being planted close together, yielded only about 
one-tenth as much grain per plant, but the variation in yield and in 
percentage of nitrogen per plant was even greater than in the 
centgeners. 

269 



16 



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18 



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Figure 6 is a graphic illus- 
tration of the centgener and 
row plats. The soil on which 
these plats were located was 
thought to be very uniform, 
and the appearance of the 
crop on the various plats was 
also uniform. The average 
per cent of nitrogen in the 
10 centgeners varied from 
2.27 (No. 41301) to 3.04 (No. 
42001). To show the loca- 
tion of high and low ni- 
trogen plants in each cent- 
gener the method of plotting 
shown in the figure was used. 
Where plants were missing 
the space is left blank; where 
a plant analyzed less than 
2.20 per cent in nitrogen a 
dot (.) is used; from 2.20 to 
2.80 per cent the circle is 
employed, denoting interme- 
diates; from 2.80 to 3 per 
cent a dash ( — ) is used; and 
all plants analyzing above 3 
per cent are marked by a 
cross ( + ) . The ' ' highs ' ' and 
"lows" tend to segregate, as 
in 1907. Also there is a pro- 
gressive increase toward one 
end of the series. The 10 
duplicate rows are plotted in 
a similar manner. The rows 
were more uniform in com- 
position than the centgeners, 
but they show a variation in 
composition from 2.58 to 2.84 
per cent of nitrogen. Also 
there seems to be no con- 
sistent relation between the 
rows and the corresponding 
centgeners, or the parent 



269 



EXPERIMENTAL ERROR AND VARIATION IN NITROGEN. 



19 



plants. The variation in both centgeners and rows seems to be 
due to local effects, and does not appear to be hereditary. We 
may eliminate any possibility of hereditary effect by adding to- 
gether the short rows in the centgeners which come end to end, 
thus making 10 long rows with each centgener equally represented. 
The results of such composite analyses are shown at the right of the 
centgener plat, indicating a variation ranging from 2.40 to 2.81 in 
percentage of nitrogen in the 10 rows. In the same way we may 
divide the 10 original rows into blocks having each row equally 
represented. Variation in the 10 blocks thus formed is shown, at 
the bottom of figure 6, to be from 2.47 to 2.85 per cent of nitrogen. 

RELATION OF YIELD OF GRAIN TO NITROGEN CONTENT. 

Since some centgeners yield more grain than others, the 29 cent- 
geners from the same parent plant, of which the 10 centgeners just 
considered were a part, were arranged according to percentage of 
nitrogen and summarized in groups of 5 centgeners. This summary 
(Table V) shows some relation between yield of grain per centgener 
and nitrogen content, the yield varying inversely with the nitrogen 
content, but when the 29 corresponding rows were arranged in the 
same way no such relation was shown. 

Table V. — Nitrogen content of 29 centgeners and corresponding rows from family No 

831 in 1908. 



Arranged according to nitrogen in centgeners. 


Arranged according to nitrogen in rows. 


CD 

a 

<o 
60 


Centgener. 


Corresponding 
row. 


Nitrogen in parent 
plants. 


is 

o 

Ih 

o 

hi 
g 

a 

3 


Row. 


Corresponding 
centgener. 


a 

0J 

E. 

ft 


a 

3 

o 

"o 
t-> 

CD 

a 

3 


a 

CD 

60 

o 


2 

»>. 

"3 

o 


Average yield 
per plant. 


a 

o 
o 


CD 

">. 
o 


a 

<x> 

to 

£ 


2 
'P. 

o 


a 

a> 
so 
o 

M 


2 

« 

O 

Eh 


2 
■pVa 

v | 
> ft 


s-8 

•- a 

aft 

CD 

bo 
o 


5. , 

5 

5 
5 , 

5 
4 


P. ct. 

2.83 
2.63 
2.56 
2.52 
2.-14 
2.34 


Grams, 
616 
614 
851 
767 
799 
916 


Grams. 
7.19 
7.13 
9.60 
9.01 
9.01 
10.50 


P.ct. 
2.67 
2.66 
2.65 
2.57 
2.52 
2.64 


Grams. 
194 
200 
173 
179 
189 
209 


Per cent. 
2.69 
2.68 
2.63 
2.66 
2.71 
2.68 


5 

5 
5 
5 
5 
4 


P.ct. 
2.78 
2.72 
2.65 
2.60 
2.55 
2.35 


Grms. 
189 
196 
194 
195 
188 
176 


P. ct. 
2.63 
2.57 
2.52 
2.57 
2.55 
2.50 


Grms. 
652 
763 
817 
789 
777 
729 


Grms. 
7.52 
9.03 
9.14 

11.13 
8.72 
8.50 


P. cf. 
2.65 
2.73 
2.72 
2.62 
2.64 
2.68 



269 



20 EXPERIMENTS IN WHEAT BREEDING. 

Table VI. — Nitrogen content and yield of grain from ISO wheat plants, arranged in inverse 

order of percentage of nitrogen, in groups of 10. 
Ninety Plants from Centgenek No. 41801. 



I'lunt No. 


Nitro- 
gen. 


Yield. 


Plant No. 


Nitro- 
gen. 


Yield. 


Plant No. 


Nitro- 
gen. 


Yield. 


52 


Per ct. 

3.44 
3.22 
3.21 
3.19 
3.19 
3.17 
3.13 
3.00 
2.98 
2.98 


Grams. 

1.55 
. 60 

7.86 
4.36 
6.45 
7.92 
4.89 
13.42 
10.6.5 
7.54 


64 


Per ct. 
2.62 
2.62 
2.62 
2.61 
2.61 
2.60 
2.60* 
2.58 
2.58 
2.58 


Grams. 
11.11 
16.23 
19.49 
9.16 
1.20 
7.00 
3.11 
8.22 
6.45 
6.76 


27 


Per ct. 
2.43 
2.43 
2. 43 
2. 43 
2.41 
2.41 
2.40 
2.39 
2.39 
2.39 


Grams. 
7.49 


79 


83 


47 


7.11 


01 


93 


59 

78 

26 

63 


6.60 


81 


9 


7.39 


91 


51 


7.48 


41 


31 


14.83 


22 


67 


20 


10.37 


L2 


8 




8.82 


6 


16 


48 


1.44 


01 


54 


69 


8.40 




Average. 

56 

60 

73 

76 

32 

95 

14 

18 


Average. . . . 
68 






3.15 


6.52 


2.60 


8.87 


2.41 


7.99 


71 


2.92 

2.92 
2. 89 

2.85 
2.82 

2.82 
2.79 
2. 78 

2.77 
2.77 


2.46 

10.52 
9.14 
7.69 

11.75 
.45 

11.46 
6.82 
7.59 
4.44 


2.58 
2.57 
2.57 
2.56 
2.53 
2.51 
2. 50 
2.48 
2.48 
2.48 


6.61 
10.56 
15.31 
1.34 
8.42 
12. 25 
17.52 
11.22 
6.15 
4.69 


2.37 
2.37 
2.36 
2.34 
2.30 
2.29 
2. 29 
2.27 
2.27 
2.27 


8.00 


90 


96 


6.07 


80 


55 


8.30 


33 


24 


11.07 


72 


45 


9.59 


87 


25 


13. 16 


23 


58 


8.19 


42 


28 


7.90 


75 


49 

50 

86 

34 

43 

70 

98 


36 


8.60 


97 


44 


6.85 




Average 

39 




Average 


2.83 


7.43 


2.52 


9.41 


2.31 


8.77 


ll 


2.71 
2.70 
2.68 
2.68 
2.65 
2.65 
2.65 
2. 65 
2.65 
2.62 


11.47 
6.83 

10. 52 
6.32 
5.55 

14.26 
7.45 
5.21" 

16.94 
9.17 


2.48 
2.47 
2.47 
2.47 
2.47 
2.46 
2.46 
2.46 
2.44 
2.43 


10.01 
21.10 
11.18 
13.25 

6.83 
12.08 

8.27 
12.81 

2. 93 
16.20 


2.26 
2.25 
2. 23 
2.22 
2.20 
2.20 
2. 20 
2.11 
2.11 
2.09 


8.66 


74 


29 


9.85 


21 


30 


9.17 


85 


46 


7.24 


15 


37 


10.01 


53 


40 

77 


57 


14.78 


84 


89 


13.50 


88 


99 

10.. ..r 


17 


10.31 


94 


19 


10.40 


7 


5 


38 


6.90 




Average 


Average 






2.66 


9.47 


2.46 


11.47 


2.19 


10.08 







Ninety Plants from Row No. 141801. 






79 


3.31 
3.29 
3.25 
3.20 
3.19 
3.18 
3.18 
3.17 
3.10 
3.09 


0.84 
.26 
.30 
.35 
.77 
.44 
.79 

1.94 
.33 
.96 


88 


2.77 
2.76 
2.76 
2.76 
2.75 
2.74 
2.74 
2.71 
2.69 
2.67 


0.56 

1.69 

1.08 

3.41 

1.29 

2.51 

1.30 

.53 

.63 

.18 


25 

31 


2.54 
2.54 
2.54 
2.53 
2.53 
2. 52 
2.51 
2.48 
2.48 
2. 47 


0.87 




8 


1.54 




18 

99 


40 

72 


1.07 


11 


1.72 




49 

46 

89 


2. 42 


76 


77 

62 


.10 




.66 


5 


15 

38 

10 

Average. 

50 

32 

64 

93 

97 

47 

78 

50 

70 

51 

Vverage. . . . 

74 

26 

54 

63 

34 

56 

86 




1.62 


87 




4.32 


U 


69 


2. 00 




81 






3.20 


.70 


2.73 


1.32 


2.51 


1.63 


S3 


3.09 
3.08 

3.07 
3.05 
3.02 
3.00 
2. 09 
2.96 
2.90 
2.88 


.30 

.65 

.79 

.69 

2.37 

.77 

2. 27 

1.59 

1.28 

2.02 


2.67 
2. 66 

2.66 
2.66 
2.65 
2.64 
2. 64 
2.63 
2.62 
2.61 


.65 

1.01 

1.21 

1.29 

7.76 

.70 

.45 

.74 

.57 

2.01 


2.47 

2. 47 
2. 45 
2. 45 
2.44 
2.43 
2.39 
2.39 
2.39 
2.35 


1.46 


16 




2.07 


17 


37 

39 


.60 


20 


.81 


23 


98 


7.10 


12 


41 


2.33 


21 


42 


2. 74 


27 


44 


2.22 


85 


58 


.86 


90 


52 


1.12 




Average.. . 
71 




Average.. .. 


3.00 


1.27 


2.64 


1.64 


2.42 


2.13 


68 


2.87 
2.84 
2.82 
2.80 
2.80 
2.79 
2.79 
2.77 
2.77 
2.77 


1.42 

2.34 

1.61 

.52 

.24 

.88 

1.48 

.65 

1.92 

.52 


2.61 
2.60 
2.60 
2.60 
2.58 
2.58 
2.58 
2.58 
2.57 
2.56 


1.07 

1.18 

.10 

.94 

.99 

.38 

.90 

2.50 

2.16 

2.31 


2.33 
2.30 
2.29 
2.25 
2.18 
2.14 
1.99 
1.87 
1.37 
1.33 


1.39 


30 


91 


.81 


29 


61 


.20 


6 


48 


1.17 


60 .. 


24 


.21 


55 .. 


43 


1.31 


84 


36 


1.13 


22 


96 

28 

67 

Average. . 


45 


1.07 


53 


94 


.79 


75 .. 


19 


.47 




Average . . 




Average 


2.80 


1.14 


2.59 


1.25 


2.00 


.85 



269 



EXPERIMENTAL ERROR AND VARIATION IN NITROGEN. 



21 



Table VI. — Nitrogen content and yield of grain from ISO wheat plants, arranged in in vene 
order of percentage of nitrogen, in groups of 10 — Continued. 
Summary of Averages. 



Group 


Croups from cent- 
gener No. 41801. 


Groups from row 
No. 141801. 


Group 
No. 


Groups from cent- 
gener No. 41801. 


Groups from row 
No. 141801. 


No. 


Nitrogen. 


Grain per 
plant. 


Nitrogen. 


Grain per 
plant. 


Nitrogen. 


Grain per 
plant. 


Nitrogen. 


Grain per 
plant. 


1 


Per cent. 
3. 15 
2. S3 
2. 66 
2.60 
2.52 


Grams. 
6.52 
7.43 

9.47 
s. 87 
9.41 


Per cent. 
3.20 
3.00 
2.80 
2.73 
2.64 


Grams. 
0.70 
1.27 
1.14 
1.32 
1.64 


6 


Per cent. 
2. 40 
2.41 

2.31 
2. 19 


Grams. 
11.47 
7.99 

8.77 
10. OS 


Per ct m. 
2.59 
2.51 
2.42 
2.00 


Grams. 
1. 25 


2 


7 


1.63 


3 


8 


2.13 


4 


9 


. 85 


.5 

















The fluctuation in yield between plants within a centgener or row 
commonly varies as much as 500 per cent. To note whether this 
wide variation bore any relation to nitrogen content, the results from 
all the plants in centgener No. 41801 and from its corresponding row 
were tabulated according to nitrogen content (Table VI). While 
the summary shows a marked variation in nitrogen content, there is 
no corresponding change in yield, although there is a slight irregular 
tendency for yield to increase as nitrogen decreases. 

While the foregoing data deal almost entirely with variations under 
nursery conditions, it would be interesting to know whether such local 
variations also occur under field conditions. That individual plants 
vary in this way is without doubt true, as the records of the row plats 
just cited show. To determine whether local variations were found 
in field plats, two sets of data were secured in the following manner: 

In one of the field plats a drill row 224 feet long was selected and 
divided into 2-foot sections. The soil was of average fertility and 
uniformity. . The results are shown in Table VIII. 

Also a plat of land 77 by 88 feet with a 5-foot margin outside of this 
was sown to Turkey winter wheat, using a drill 5.5 feet wide. A very 
uniform stand and quite uniform growth were secured. The plat 
would have yielded about 30 bushels per acre. At harvest time it 
was divided into blocks 5.5 feet square, making 224 such blocks. A 
composite sample was made from the harvest of each block and each 
sample was analyzed for total nitrogen. Figure 7 is a diagram of this 
plat, showing the yield of grain and percentage of nitrogen in each 
block. The same variation is here found that has been noted hereto- 
fore in the centgeners and nursery rows. For example, in the first 
series of 16 blocks, Nos. 2 and 13 average 1.74 per cent of nitrogen, 
while Nos. 3 and 8 average 2.07 per cent. This variation seems large 
in view of the fact that each block has an average of 600 to 800 plants. 
In this case the variation must be due to some local soil condition. 
When different numbers of blocks are grouped, the resulting areas are 
of considerable size, as illustrated by figure 8. The plats shown at B 
are 11 by 22 feet in area and each was sampled 8 times, yet they show 
a variation in nitrogen content ranging from 1.81 to 1.97 percent. 

269 



22 



EXPERIMENTS IN WHEAT BREEDING. 



REDUCING THE EXPERIMENTAL ERROR. 

So great is the fluctuation in individual plants, due to variation in 
environment, that there would seem to be no hope of improving the 

percentage of nitrogen 



/eo /.&3 



£80 

221 



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222 



£.89 

ggi 



2 00 
220 



£96 

219 



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218 



2.03 
217 



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210 



£93 

209 



207 



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206 



£96 

205 



204 



203 



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202 



200 



£.94 

198 



£87 



£83 

194 



£.86 



£.83 

190 



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182 



£.82 



£87 
167 



£96 

162 



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129 



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125 



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£.85 



£82 



£86 



2.00 
6? 



207 

a. 



through the continu- 
ous selection of high 
fluctuates. No cumu- 
lative results can be 
expected where the 
error is larger than the 
expected variation. 

The problem of find- 
ing a high -nitrogen 
wheat seems to resolve 
itself into the isolation 
of pure strains and the 
comparison of these for 
nitrogen content. To 
effect this isolation and 
comparison, a method 
must be found that will 
reduce error to the 
minimum. R eplic a- 
tion according to some 
systematic method 
seems the most prac- 
tical way. A num- 
ber of examples have been worked up from data at .hand to illus- 
trate the effect of replication in reducing error. 

^ & C 



£83 

50 



£96 



2.0* 



204 



£8S 



£.86 



£87 



£75 

2 



2.06 



Fig. 7.— Diagram of plat of Turkey wheat containing 224 blocks (each 
5.5 feet square), showing the location of each block (lower figures) and 
variations in the percentage of nitrogen in the grain (upper figures). 



£98 



SI 



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90 


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Fig. 8. — Diagrams of plats of Turkey wheat, showing the arrangement of 224 blocks (each 5.5 feet square) 
when combined in groups of adjacent blocks, with average nitrogen content for each group: A , Groups of 
4; B, groups of 8; C, groups of 16. 



REPLICATION OF SINGLE PLANTS. 



In the first case the 840 centgener plants from the same parent, 
heretofore referred to (fig. 6), were grouped in various ways. Starting 

269 



EXPERIMENTAL ERROR AND VARIATION IN NITROGEN. 



23 



with the first plant and taking every forty-second plant thereafter 
gave a composite group of 20 plants. Taking the second and every 
forty-second thereafter in the same way gave a second group, and 
so on in the same manner until 42 groups of 20 plants each had been 
made. In a similar manner 21 groups of 40 plants each were formed. 
Also, each of the 10 centgeners, being 10 plants square, was formed 
into 10 rows and the rows numbered 1 to 10. Each row would have 
10 plants if the stand were perfect, but in this case it averaged only 8.4 
plants per row. By combining the first rows, second rows, etc., in the 
10 centgeners, 10 groups were made of 10 rows, or 84 plants each. The 
results of the above combinations are shown in Table VII. Where 
20 plants, uniformly distributed, were combined, the variation in 
nitrogen content was from 2.40 to 2.67 per cent. Where 40 plants 
were combined, the variation ranged from 2.47 tro 2.60 per cent, but 
the 10 groups of 10 rows each varied only from 2.49 to 2.59 per cent. 
Just what should constitute the limits of error in any case will depend 
on the minimum limit of the variations which are to be detected. 
In this case 0.1 per cent of nitrogen might be considered such a limit. 

Table VII. — Nitrogen content of 90 -plants of Turkey wheat from 1 centgener and of 
840 plants variotisly combined into groups to show deviation from mean. 

















840 single plants variously combined into groups. 














Com bination 


Com bination 


90 single plants in 1 centgener 
(united when having same nitro- 
gen content). 


Combination 1.— Four groups, 
each composed of every 42d 
plant in 10 centgeners, or 20 
plants. 


2. — T w 
groups , each 
composed of 
every 21st 
plant in 10 


3. — A group 
composed of 
every 10th 
row in 10 
cent geners 
or 10 rows, 




— 














centgeners, 
or 40 plants. 


equaling 84 
plants. 




>> 


c 




>. 




c 






a 






p 




c 




a 


a 


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a 


- 







a 







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a 










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M 
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a 

a 
— 




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<v 
M 

O 




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to 






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be 




S 


bo 




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is 


£ 


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H 


— 




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h 


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£ 


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© 











03 






£ 


fe 


Q 


k 


£ 




O 


Sz; 




S 


k 







Sz; 


n 


fc 


fi 


P.ct. 






Per ct. 








Per ct. 






Per ct. 






Per ct. 




Per ct. 




2.09 


1 


-0. 482 


2.58 


4 


+0.CC 


2.47 


-0.04 


2.44 


-0.08S 


2.48 


-0.044 


2.49 


-0.042 


2.11 


2 


- .462 


2.60 


3 


+ 


.028 


2.47 


— 


.043 


2.51 


_ 


.019 


2.49 


- .034 


2.51 


- .022 


2.20 


3 


- .372 


2.61 


2 


+ 


.038 


2.48 


— 


.033 


2.51 


_ 


.019 


2.50 


- .024 


2.52 


- .012 


2.22 


1 


- .352 


2.62 


4 


+ 


.048 


2.50 


— 


.013 


2.51 


^_ 


.019 


2.52 


- .004 


2.52 


- .012 


2.23 


1 


- .342 


2.65 


5 


+ 


.078 


2.51 


— 


.003 


2.51 - 


.019 


2.52 


- .004 


2.53 


- .002 


2.25 


1 


- .322 


2.68 


2 


+ 


.108 


2.51 


— 


.003 


2.51 


_ 


.019 


2.53 


+ .006 


2.53 


- .002 


2.26 


1 


- .312 


2.70 


1 


+ 


.128 


2.53 


+ 


.017 


2.52 


+ 


.009 


2.53 


+ .006 


2.53 


- .002 


2.27 


3 


- .302 


2.71 


1 


+ 


.138 


2.54 


+ 


.027 


2.59 


+ 


.061 


2.53 


+ -006 


2.54 


+ .008 


2.29 


2 


- .282 


2.77 


2 


+ 


.198 


2.54 


+ 


.027 


2.59 


+ 


.061 


2.55 


+ .036 


2.56 


+ .028 


2.30 


1 


- .272 


2.78 


1 


+ 


. 20S 


2.58 


+ 


.067 


2.60 


+ 


.071 


2.59 


+ .066 


2.59 


+ .058 


2.34 


1 
1 

3 


- .232 

- .212 

- .202 


2.79 
2.82 
2.85 
2.89 


1 
2 
1 


+ 
+ 
+ 
+ 


.218 
.248 
.278 
.318 






















2.36 
2.37 


2.513 


.0276 


2.529 


.0386 


2.524 


.023 


2. 532 


.0188 


2.39 


3 


- ! 182 


1 


2.46 


_ 


.092 


2.40 




.128 


2.47 


- .07 






2.40 


1 


- .172 


2.92 


2 


+ 


.348 


2.51 


— 


.042 


2.48 


_ 


.048 


2.48 


- .06 






2.41 


2 


- .162 


2.98 


2 


+ 


.408 


2.52 


— 


.032 


2.50 


_ 


.C28 


2.48 


- .06 






2.43 


5 


- .142 


3.00 


1 


+ 


.428 


2.52 


— 


.032 


2.52 





-008 


2.50 


- .04 






2.44 


1 


- .132 


3.13 


1 


+ 


.558 


2.54 


— 


.012 


2.53 


+ 


.002 


2.53 


- .01 






2.46 


3 


- .112 


3.17 


1 


+ 


.598 


2.54 


— 


.012 


2.54 


+ 


.012 


2.53 


- .01 






2.47 


4 


- .102 


3.19 


2 


+- 


.618 


2.54 


— 


.012 


2.54 


+ 


.012 


2.54 


00 






2.48 


2 


- .092 


3.21 


1 


+ 


.638 


2.58 


+ 


.028 


2.56 


+ 


.032 


2.54 


.00 






2.50 


1 


- .072 


3.22 


1 


4- 


.648 


2.64 


+ 


.088 


2.56 


4. 


!o32 


2.56 


+ .02 






2.51 


1 


- .062 


3.44 


1 


+ 


.868 


2.67 


+ 


.118 


2.57 


-j- 


.042 


2.60 


4- .06 






2.53 


1 


- .042 
















2.57 


+ 


!042 


2.61 


+ .07 


















2.56 


1 


— .012 


2.572 






.214 


2.552 




.0468 


2.58 
2.528 










2?57 


2 


- .002 


- 






+ 


.052 


2.54 


.0364 








.0365 





269 



24 



EXPERIMENTS IN WHEAT BREEDING. 



Where the plants were repeated 20 and 40 times the error was 
almost what we might reasonably expect the actual variation in 
pure strains to be, but where 10 centgener rows, or 84 plants, were 
combined the extreme error was within bounds. The data would 
indicate that single plants would have to be replicated nearly 100 
times to bring: the variation within the limits of error. 



REPLICATION OF 2-FOOT ROWS. 

Table VIII illustrates the variation to be expected by replicating 
2-foot rows. For these data a single 220-foot drill row in the general 
wheat field was divided into 2-foot sections and a composite sample 
made of each section. The sections were combined in two different 
ways. The first combination was composed of every twenty-second 
section, making 22 groups of 5 sections each, and the second com- 
bination was composed of every eleventh section, making 11 groups 
of 10 sections each. 

Here, again, the extremes are rather wide, but if these are excluded 
the results would be called satisfactory. If a comparison of pure 
strains of wheat was being made under similar conditions, it would 
be necessary to take for further trial the entire best half of the strains 
tested in order to be within the limit of error. (See p. 30 and fig. 9.) 

Table VIII. — Nitrogen content of 110 2-foot sections of drill row of Turkey wheat, 
arranged in order of -percentage of nitrogen and also in groups of 5 and 10, to show devia- 
tion from mean. 















Five rows in a 


Ten rows in a group 


Single 2-foot rows (those with same nitrogen contenl 


united). 


group composed 


compos 


3d of every 














of every 22d row. 


11th row. 


Nitro- 


Fre- 


Devia- 


Nitro- 


Fre- 


Devia- 


Nitro- 


Devia- 


Nitro- 


Devia- 


gen. 


quency. 


tion. 


gen. 


quency. 


tion. 


gen. 


tion. 


gen. 


tion. 


Per cent. 






Per cent. 






Per cent. 




Per cent. 




1. 76 




-0. 271 


2.04 


5 


+0.009 


1.91 


-0. 109 


1.96 


-0. 069 


1.79 




- .241 


2.05 


2 


+ .019 


1.96 


- .059 


1.98 


- .049 


1.81 




- .221 


2.06 


4 


+ .029 


2.01 


- .009 


1.98 


- .049 


1.85 




- .181 


2.07 


5 


+ .039 


2.01 


- .009 


2.00 


- .029 


1.86 




- .171 


2.08 


4 


+ .049 


2.01 


- .009 


2.02 


- .009 


1.87 




- .161 


2.09 


3 


+ .059 


2.02 


+ .001 


2.03 


+ .001 


1.88 




- .151 


2.10 


6 


+ .069 


2.02 


+ .001 


2.04 


+ .011 


1.89 




- .141 


2.11 


1 


+ .079 


2.03 


+ .011 


2. 06 


+ .031 


1.90 




- .131 


2.12 


2 


+ .089 


2.06 


+ .041 


2.06 


+ .031 


1.91 




- .121 


2.13 


2 


+ .099 


2.09 


+ .071 


2.06 


+ .031 


1.92 




- .111 


2.14 


3 


+ .109 


2.09 


+ .071 


2.13 


+ .101 


1.93 


5 


- .101 


2.15 


1 


+ .119 


















1.95 


5 


- .081 


2.16 


1 


+ .129 


2.019 


.0355 


2.029 


. 0374 


1.96 
1.97 


3 
2 


- .071 

- .061 


2.17 
2.19 


1 
2 


+ .139 
+ .159 










1.96 


- .077 






1.98 


5 


- .051 


2.20 


3 


+ .1C9 


1.98 


- .057 






1.99 


2 


- .041 


2.26 


4 


+ .229 


1.99 


- .047 






2.00 


4 


- .031 


2.28 


1 


+ .249 


1.99 


- .047 






2.01 


7 


- .021 


2.37 


1 


+ .339 


2.03 


- .007 






2.02 
2.03 


2 
6 


- .011 

- .001 








2.03 
2.04 


- .007 
+ .003 






2.031 




+ .093 


















2.05 


+ .013 


















2.08 


+ .043 


















2.09 


+ .053 


















2.17 


+ .133 








2.037 


.0443 





269 



EXPERIMENTAL ERROR AND VARIATION IN NITROGEN. 



25 



REPLICATION OF 16-FOOT ROWS. 

Since 16-foot rows are frequently used as test plats, a determina- 
tion was made of the variation in a series of these. One hundred 
check plats from the 1909 field nursery were grouped by fives and 
tens in the same manner as in the two cases just cited. The results 
are shown hi Table IX. The coefficient of variability and also the 
extreme variation are less than in the cases just considered. 

Table IX. — Nitrogen content of 100 16-foot rows of Turkey wheat, all from the same seed, 
arranged singly in order of percentage of nitrogen and also in groups of 5 and 10, to 
show deviation from mean. 















Five rows in a 


Ten rows in a group 


Single 16-foot rows (those with same nitrogen content united). 


group composed 


composed of every 














of every 20th row. 


10th row. 


Nitro- 


Fre- 


Devia- 


Nitro- 


Fre- 


Devia- 


Nitro- 


Devia- 


Nitro- 


Devia- 


gen. 


quency. 


tion. 


gen. 


quency. 


tion. 


gen. 


tion. 


gen. 


tion. 


Per cent. 






Per cent. 






Per cent. 




Per cent. 




1.82 


1 


-0.316 


2.18 


6 


+0.044 


2.09 


-0.050 


2.10 


-0. 037 


1.86 


2 


- .276 


2.20 


1 


+ .064 


2.11 


- .036 


2.11 


- .027 


1.87 


1 


- .266 


2.21 


1 


+ .074 


2.13 


- .016 


2.12 


- .017 


1.89 


1 


- .246 


2.22 


4 


+ .084 


2.13 


- .016 


2.13 


- .007 


1.92 


2 


- .216 


2.23 


1 


+ .094 


2.13 


- .010 


2.14 


+ .003 


1.93 


2 


- .200 


2.25 


2 


+ .114 


2.14 


- .000 


2.14 


+ .003 


1.94 


1 


- .196 


2.27 


2 


+ .134 


2.16 i + .014 


2.15 


+ .013 


1.96 


3 


- .176 


2.28 


2 


+ .144 


2.17 + .024 


2.15 


+ .013 


1.97 


2 


- .166 


2.29 


3 


+ .154 


2.19 1 + .044 


2.15 


+ .013 


1.99 


1 


- .140 


2.31 


3 


+ .174 


2.21 + .064 


2.18 


+ .043 


2.00 
2.01 


3 
1 


- .136 

- .126 


2.34 
2.35 


2 

1 


+ .204 
+ .214 








2.146 1 .0292 


2.137 


.0176 


2.03 
2.04 


5 
3 


- .100 

- .096 


2.36 
2.38 


1 

1 


+ .224 
+ .244 








2.07 i - .058 






2.06 


6 


- .076 


2.42 


1 


+ .284 


2.08 - .048 






2.07 


2 


- .086 


2.43 


1 


+ .294 


2.09 1 - .038 






2.08 


6 


- .056 


2.45 


1 


+ .314 


2.09 - .038 






2.10 


3 


- .036 


2.48 


1 


+ .344 


2.10 


- .028 






2.11 


2 


- .026 


2.50 


1 


+ .364 


2.13 


+ .002 






2.13 


7 


- .006 


2.52 


1 


+ .384 


2.17 


+ .042 






2.14 
2.15 


2 
4 


+ .004 
+ .014 








2.18 
2.18 


+ .052 
+ .052 






2.136 




.1178 






2.17 


4 


+ .034 








2.19 


+ .062 








2.128 


.0420 





Where the 16-foot rows were repeated 10 times the extreme dif- 
ference in nitrogen content was only 0.08 per cent. To further test 
this question, 500 rows, each 16 feet in length, were planted in the 
fall of 1909 under quite uniform conditions. These rows were har- 
vested and combined in groups of 5, 10, 15, and 20, as in the previous 
case. The results are summarized at the bottom of Table X. When 
the rows are repeated only 5 times the error is too wide for satisfac- 
tory results, but when repeated 10 times the error is small enough 
for experimental purposes. Repeating 15 and 20 times gave only a 
small further reduction in variation. 

A point of interest is the fact that in 1909, where rows were repeated 

5 or 10 times, the experimental error was less than it was hi 1910. 

In fact, there is no way of establishing a set rule as to the number 

of repetitions necessary, since the experimental error is influenced by 

69826°— Bui. 269—13 4 



26 



EXPERIMENTS IN WHEAT BREEDING. 



all the factors affecting the growth of plants, such as soil fertility, 
climate, or insects. In order to know what this error is in a par- 
ticular case it would be advisable to grow a sufficient number of 
check plats in each system of plats to determine the error by actual 
test. 

Table X is a summary of results with the systematic repetition of 
plants and rows. The column under "Coefficient of variability" 
shows that repeating 20 single plants in a systematic way has given 
about as great accuracy in determining nitrogen content as 2-foot 
rows repeated 10 times or 16-foot rows repeated 5 times. For deter- 
mining comparative nitrogen content, repeating single plants 20 to 
40 times in a systematic method seems to give quite satisfactory 
results. 

Table X. — Summary showing degree of error due to variation in environment, according 
to several methods of comparison. 



Classification. 


Number 

of 
groups. 


Mean 
nitrogen 
content. 


Extreme 
variation. 


Average 
devia- 
tion. 


Standard 
devia- 
tion. 


Coeffi- 
cient of 
varia- 
bility. 


90 single plants (Table VII) 


90 


Per cent. 
2.572 


2. 09-3. 44 


0. 2140 


0.279 


Per cent. 
10.85 






840 single plants (Table VII): 

Every 42d plant, 20 plants in a 


f a 10 
1 blO 
1 c 10 
I dl2 


2.513 

2.552 
2.529 
2.528 


2.47-2.58 
2. 46-2. 67 
2. 44-2. 60 
2. 40-2. 58 


.0276 
.0468 
.0386 
.0365 


.0335 
.0592 
.0473 
.0484 


1.33 
2.32 

1.87 




1.91 




10.5 


2.531 


2. 44-2. 61 


.0374 


.0471 


1.86 






Every 21st plant, 40 plants in a 


/ a 10 
\ bll 


2.524 
2.540 


2. 48-2. 59 
2. 47-2. 61 


.0230 
.0364 


.0307 
.0455 


1.22 
1.17 








10.5 


2.532 


2. 47-2. 60 


.0297 


.0381 


1.50 






As 10 centgeners, every 10th cent- 
gener row, 10 rows in a group 


10 

110 


2. 532 


2. 49-2. 59 


.0188 


.0260 


1.03 


110 2-foot rows, single rows (Table VIII). 


2.031 


1.76-2.37 


.093 


.1087 


5.35 


Every 22d row, 5 rows in a group 


1 all 
\ bll 


2.019 
2.037 


1.91-2.09 
1.96-2.17 


.0355 
.0443 


.0499 
.0574 


2.47 
2.82 




11 

11 
100 


2.028 


1.94-2.13 


.0399 


.0537 


2.65 






Every 11th row, 10 rows in a group.. 


2.029 


1.96-2.13 


. 0374 


.0464 


2.28 


100 16-foot rows (Table IX) 


2.136 


1.82-2.52 


.1178 


.1492 


6.98 






Every 20th row, 5 rows in a group.. . 


/ a 10 
\ blO 


2.146 
2.128 


2. 09-2. 21 
2. 07-2. 19 


.0292 
.0420 


. 0347 
.0451 


1.62 
2.12 




10 


2.137 


2. 08-2. 20 


.0356 


.0399 


1.87 






Every 10th row, 10 rows in a group. . 
500 16-foot rows (in 1910): 


10 


2.137 

1.905 
1.904 
1.917 
1.908 
1.890 


2. 10-2. 18 

1.68-2. 28 
1.81-1.99 
1.84-2.02 
1.81-2.03 
1.81-1.98 


.0176 

.0859 
.0393 
.0376 
.0403 
.0388 


.0219 

.1080 
.0469 
.0469 
.0502 
.0488 


1.02 
5.67 


Every 100th row, 5 rows in a group.. 


f a 25 
1 b25 
1 c 25 
1 d25 


2.46 
2.45 
2.63 
2.42 




1.905 


1.82-2.00 


.0379 


.0474 


2.49 




/ a 25 
\ b25 




Every 50th row, 10 rows in a group. . 
Every 33d row, 15 rows in a group ... 


1.908 
1.902 
1.905 
1.905 


1.S3-1.96 
1.83-1.96 
1.86-1.96 
1.85-1.96 


.0273 
.0286 
. 0235 
.0190 


.0329 
. 0343 
.0276 
.0242 


1.72 
1.80 
1.45 






1.27 









269 



EXPERIMENTAL ERROR AND VARIATION IN NITROGEN. 



27 



THE SMALL-BLOCK TEST. 

Figure 7 (p. 22) illustrates the method of making the small-block 
test and also shows the percentage of nitrogen in the grain from 
each block. Table XI shows the result of repeating these blocks 4, 
8, and 16 times in a systematic method, i. e., taking every fifty-sixth, 
twenty-eighth, or fourteenth block (fig. 8). The experimental error 
varied inversely with the number of repetitions, but was only within 
the limit of error when the repetition was 16 times. 



Table XI. — Nitrogen am i '.ent of Turkey wheat grovm in 224 block plats {each 5 .5 feet 

square) in 1909 and 1910. 

Systematically Repeated to Form Groups of 4, S, and l(i Blocks. 



Four blocks 


in a group composed of 


3very 56th 


Eight blocks in a group 
composed of every 


Sixteen blocks in a group 
composed of every 










28th block. 


14th block. 


Nitrogen. 


Deviation. 


Nitrogen. 


Deviation. 


Nitrogen. 


Deviation. 


Nitrogen. 


Deviation. 


Per cent. 




Per cent. 




Per cent. 




Per cent. 




1.78 


-0. 128 


LSI 


-0.115 


1.S2 


-0. 096 


1.84 


-0.06 


1.84 


- .068 


1.85 


- .075 


1.87 


- .046 


1.86 


- .04 


1.85 


- .058 


1.87 


- .055 


1.88 


- .036 


1.87 


- .03 


1.88 


- .028 


1.87 


- .055 


1.90 


- .016 


1.87 


- .03 


1.89 


- .018 


1.90 


- .025 


1.90 


- .016 


1.89 


- .01 


1.90 


- .008 


1.93 


+ .005 


1.90 


- .016 


1.90 


+ .00 


1.91 


+ -002 


1.93 


+ .005 


1.92 


+ .004 


1.90 


+ .00 


1.91 


+ .002 


1.96 


+ .035 


1.92 


+ .004 


1.91 


+ .01 


1.93 


+ .022 


1.96 


+ .035 


1.94 


+ .024 


1.91 


+ .01 


1.93 


+ .022 


1.96 


+ .035 


1.94 


+ .024 


1.92 


+ .02 


1.94 


+ .032 


1.96 


+ .035 


1.94 


+ .024 


1.92 


+ .02 


1.95 


+ .042 


1.97 


+ .045 


1.95 


+ .034 


1.93 


+ .03 


1.98 


+ .072 


1.97 


+ .045 


1.95 


+ .034 


1.94 


+ .04 


2.02 


+ .112 


2.01 


+ .085 


1.99 


+ .074 


1.94 


+ .04 


Av'ge.. 1.908 


.0439 


1.925 


.0464 


1.916 


.032 


1.90 


.024 


1.83 


- .041 


1.80 


- .094 


1.83 


- .051 






1.83 


- .041 


1 . 86 


- .034 


1.85 


- .031 






1.83 


- .041 


1.87 


- .024 


1.86 


- .021 






1.84 


- .031 


1.87 


- .024 


1.86 


- .021 






1.84 


- .031 


1.87 


- .024 


L.86 


- .021 






1.85 


- .021 


1.88 . 


- .014 


1.S7 


- .011 






1.85 


- .021 


1.89 


- .004 


1.88 


- .001 






1.86 


- .011 


1.90 


+ .006 


1.88 


- .001 






1.87 


- .001 


1.90 


+ .006 


1.88 


- .001 






1.87 


- .001 


1.90 


+ .006 


L.89 


4- .011 






1.88 


+ .009 


1 . 90 


+ .006 


1.90 


4- .021 






1.94 


+ .069 


1.90 


4- .006 


1.92 


+ .041 






1.95 


+ .079 


1.94 


+ .046 


1.92 


+ .041 






1.95 


+ .079 


2.04 


+ .146 


1.93 


+ .051 






Av'ge. .1.871 


.034 


1.894 


.0314 


1.881 


.0231 







269 



28 



EXPERIMENTS IN WHEAT BREEDING. 



Table XI. — Nitrogen content of Turkey wheat grown in 224 block plats {each 5.5 feet 
square) in 1909 and 1910 — Continued. 

Combined in* Groups of 4, 8, and v> Adjacent Blocks, to Show the Effect of Size of Plat on 

Variability. 



Two sets of 14 groups, 

Four sets of 14 groups, with 4 adjacent blocks in each with 8 adjacent 
group. blocks in each 

group. 


One set of 14 groups, 
with 16 adjacent 
blocks in each 
group. 


Nitrogen. 


I >evia- 
tion. 


Stand- 
arc t 

devia- 
tion. 


Nitro- 
gen. 


Devia- 
tion. 


Stand- 
ard , Nitro- 

devia- gen. 
tion. 


Devia- 
tion. 


Stand- 
ard 

devia- 
tion. 


Nitro- 
gen. 


Devia- 
tion. 


Stand- 
ard 

devia- 
tion. 


Per cent. 
1.79 
1.84 

1.86 
1.88 
1.91 
1.91 
1.92 
1.92 
1.93 
1.93 
1.93 
1. 94 
1.96 
1.98 


-0.117 

- .0(17 

- .047 

- .027 
+ .003 
+ .003 
+ .013 
+ .013 
-f .023 
+ .023 
+ -023 
+ .033 
+ .053 
+ .073 





Per ct. 

1.86 
1.87 
1.87 
1.88 
1.88 
1.89 
1.90 
1.90 
1.91 
1.91 
1.95 
1.95 
1.97 
1.98 


-0. 05 

- .04 

- .04 

- .03 

- .03 

- .02 

- .01 

- .01 



+ .04 
+ .04 
+ .06 
+ .07 




Per ct. 
1.81 
1.83 
1.87 
1.88 
1.89 
1.89 
1.90 
1.92 
1.92 
1.92 
1.92 
1.93 
1.93 
1.94 


-0. 0S6 

- .066 

- .026 

- .016 

- .006 

- .006 
+ .004 
+ .024 
+ .024 
+ .024 
+ .024 
+ .034 
+ .034 
+ .044 




Perct. 
1.82 
1.85 
1.85 
1.88 
1.89 
1.90 
1.90 
1.90 
1.90 
1.91 
1.93 
1.94 
1.94 
1.95 


-0. 077 

- .047 

- .047 

- .017 

- .007 
+ .003 
+ .003 
+ .003 
+ .003 
+ .013 
+ .033 
+ .043 
+ .043 
+ .053 




Average.. 1.907 


.037 


0.048 


1.91 


.0311 


0. 0376 


1.896 


.0299 


0. 0372 


1.897 


.028 


0.0363 


1.82 


- .072 

- .052 

- .052 

- .042 

- .042 

- .012 










1.81 
1.81 
1.87 
1.87 
1.88 
1.88 


- .081 

- .081 

- .021 

- .021 

- .011 

- .011 






1.84 
1.84 
1.85 
1.85 
1.88 




1.81 
1.81 
1.81 
1.82 
1.84 
1.S7 
1.87 
1.88 
1.89 
1.90 
1.91 
1.93 
1.98 
2.03 


- .072 

- .072 

- .072 

- .062 

- .042 

- .012 

- .012 

- .002 
+ .008 
+ .018 
+ .028 
+ .048 
+ .098 
+ .148 






1.91 
1.91 
1.91 
1.91 
1.92 
1.94 
1.95 
1.96 


+ .018 
-t- .018 
+ .018 
+ .018 
+ .028 
+ .048 
+ .058 
+ .068 






1.88 
1.88 
1.90 
1.90 
1.91 
1.92 
1.97 
2.00 


- .011 

- .011 
+ .009 
+ .009 
+ .019 
+ .029 
+ .079 
+ .109 






Average.. 1.892 


.0390 


. 0436 


1.882 


.0496 


.0636 


1.891 


.0358 


.0492 





269 



EXPERIMENTAL ERROR AND VARIATION IN NITROGEN. 



29 



Table XI. — Nitrogen content of Turkey icheat grown in 224 block plats (each 5.5 feet 
square) in 1909 and 1910 — Continued. 

Summary Showing Experimental Error when Blocks are Assembled in Various Ways.. 





o 

Ml 

O 

H 
V 

,o 

B 

3 


Season of 1909. 


Season of 1910. 


Classification. 


c 

o +J 

b c 

|l 

§ 8 


a 
X 


2 a 




o . 

.2 2 

0} S3 
o > 
O 


a 

9 

t a 

ZZ a) 

5 ° 

5 


03 

- - 


fa 

* 


_ a 

T) O 
s- — . 

a > 

OS 


o . 

S'S 

O > 

O 


Systematically repeated . . 

Every 56th block, 4 
blocks in a group . . . 


1 

f a 14 
I b 14 
1 c 14 
I d 14 


P. ct. 
1.898 

1.90S 
1.871 
1.925 
1.894 


1. 68-2. 18 
1. 78-2. 02 
1. S3-1. 95 
1. 81-2. 01 
1. 80-2. 04 


0. 0786 
.0439 
.0340 
. 0464 
.0314 


0. 0981 
.0579 
.0425 
.0546 
.0503 


P.ct. 
5.17 
3.03 
2.27 
2.84 
2.61 


P.ct. 
1.866 
1.852 
1.850 
1.871 
1.885 


1. 66-2. 24 
1. 81-1. 89 
1. 79-1. 91 
1. 81-1. 92 
1. 82-2. 04 


0. 0692 
.0250 
.0300 
. 0259 
.0386 


0. 8987 
.0278 
.0342 
. 0316 
.0532 


P.ct. 
4.81 
1.50 
1.85 
1.69 
2.82 




14 


1.90 


1. 80-2. 00 


.0389 


.0513 


2.69 


1.865 


1. 81-1. 94 


.0299 


.0347 


1.96 






Every 28th block, S 
blocks in a group . . . 


1 a 14 
\bl4 

14 
14 


1.916 
1.S81 

l'.90 


1. 82-1. 99 
1.83-1.93 


.0320 
.0231 


.0438 
.0287 


2.29 
1.53 


1.863 
1.869 


1. 83-1. 89 
1.83-1.91 


. 0143 
. 0184 


.0167 
.0226 


.89 
1.21 




1. 82-1. 96 


.0275 


.0362 


1.91 


1.866 


1. 83-1. 90 


.0163 


.0196 


1.05 







Every 14th block, 16 
blocks in a group. .. 


1.90 


1.84-1.94 


.0240 


.0295 


1.55 


1.864 


1.84-1.8S 


. 0123 


.013; 


.72 


Adjacent groups: 

Four blocks in a group 


f a 14 

bl4 

1 C 14 

| dl4 


1.907 
1.892 
1.910 
1.882 


1. 79-1. 98 
1. 82-1. 96 
1.86-1.98 
1.81-2.03 


.0370 
.0390 
. 0314 
.0496 


.0480 
.0436 
.0376 
.0636 


2.52 
2.31 
1.93 
3.31 


1.929 
1.871 
1.841 
1.817 


1.80-2.02 
1. 79-1. 96 
1. 78-1. 92 
1. 77-1. 89 


.0503 
.0400 
. 0301 
.0261 


.0612 
.0484 
.0363 
.0319 


3.17 
2.59 
2.00 
1.76 




14 


1.894 


1. 82-1. 99 


.0442 


.0482 


2.54 


1.865 


1. 78-1. 95 


.0366 


.04-^6 


2.38 






Eightblocksinagroup 


/ a 14 
\ b 14 


1.896 
1.891 


1. 81-1. 94 
1. 81-2. 00 


.0299 
. 0358 


.0372 
.0492 


1.96 
2.60 


1.901 
1.829 


1. 82-1. 98 
1. 79-1. 89 


.0444 
.0263 


. 0504 
. 0299 


2.65 
1.63 




14 
14 


1.894 


1. 81-1. 97 


.0328 


.0432 


2.28 


1.865 


1. 80-1. 93 


.0353 


.0401 


2.14 






Sixteen blocks in a 


1.897 


1. 82-1. 95 


.028 


.0363 


1.91 


1.866 


1.80-1.96 


. 0403 


.0464 


2.49 







In 1910 the same set of blocks was again in wheat, and they w r ere 
again grouped in the same way, exactly the same plats being com- 
bined each year. The experimental error was less in 1910 than in 
1909, and repeating the blocks 8 times gave total variations ranging 
from 1.83 to 1.90 per cent, which is weW within the experimental 
limit. It appears that repeating the plats in this particular case 8 
times in 1910 gave as good results as repeating 16 times in 1909; in 
fact, repeating 4 times would have been almost as satisfactory. In 
the case of the 16-foot rows just described the error was least in 1909, 
while the reverse was true in regard to the error in the blocks. This 
result again illustrates the point, made in discussing the row tests, 
that sufficient check plats must be used in order to know die experi- 
mental error in any particular case. 

INCREASING THE SIZE OF PLAT. 



Table XI also illustrates the effect of increasing the size of the plat. 
While such increase ought theoretically to reduce error from the 
standpoint of increasing the number of plants and including a larger 

269 



30 EXPERIMENTS IN WHEAT BREEDING. 

number of local soil variations, yet an equal number of large plats 
reach over into new territory and include new causes for variation. 
To secure a practical illustration the 224 small blocks were combined 
into several series of larger plats by adding together adjacent plats. 
This method is illustrated in figure 8 (p. 22), and the statistical data 
are given in Table XI, a study of which shows that increasing the size 
above four adjacent blocks does not decrease the variability. In 
comparing systematic replication (Table X) with increase in size of 
plat it will be seen that the former constantly decreases variation, 
and would so continue to infinity, while the latter would not be con- 
trolled by such a law. It has been noted that the degree of variability 
was not the same when similar data were collected from different 
fields or in different years. 

Variation is not a constant factor even where conditions are quite 
uniform, as is illustrated by the four sets of 14 groups composed of 
four adjacent plats. The fluctuation of extremes is almost twice as 
great in the fourth set as in the third. 

The foregoing data can not be taken as a strict comparison of the 
different methods, as the data in each case were secured under some- 
what different conditions. They are mainly valuable in illustrating 
the expected variation when different methods of comparison are 
used. It is evident that, whatever the method used, a single plat or 
duplicate plats can not be relied on for determining the actual nitro- 
gen content of a strain or variety of wheat. The plats must be 
repeated 5 to 15 times, depending on uniformity of conditions and 
accuracy of results desired. In addition, at least a few series of 
check plats should be included in order to determine the experimental 
error as a guide to accuracy of results. 

Our experience so far indicates that the simplest and most accurate 
method is to use 16-foot rows, replicated 10 tunes, with a check plat 
every 5 or 10 rows. 

THE LIMIT OF EXPERIMENTAL ERROR. 

The above examples give some indication of the experimental 
error to be expected by the different methods. Since the experi- 
mental error depends upon the variation in environmental condi- 
tions, it is possible that conditions might be found so ideal that there 
would be practically no experimental error; also that under other 
conditions it might be greater than in the cases just cited. In all 
cases the experimental error should be determined by the use of 
check plats. With this factor known it will be possible to decide on 
some plan of selection. Figure 9 illustrates an ideal case where the 
experimental error is known. Suppose that in 10 strains of wheat 
being tested by the row method with check plats, the highest should 

269 



EXPERIMENTAL ERROR AND VARIATION IN NITROGEN. 



31 



average 3 per cent of nitrogen and the lowest 2 per cent of nitrogen, 
the remainder being distributed between. Suppose a series of checks, 
repeated in the same way as the tested strains, showed a variation 
of 2.2 per cent to 2.6 per cent, with a mean of 2.4 per cent. This 
would give an experimental error of 0.2 per cent; that is, a certain 
strain might be 0.2 per cent higher than it should be or 0.2 per cent 
lower than it should be. Let the line ab indicate the variation in 
nitrogen content obtained in the 10 strains under test. If the experi- 
mental error equaled 0.2 per cent, then No. 1 might equal either 3.2 
per cent or 2.8 per cent, and in the same way a strain analyzing 
2.6 per cent might possibly be either 2.8 per cent or 2.4 per cent. 
In other words, the strain analyzing 2.6 per cent might be just as 
good as the one analyzing 3 per cent. Therefore, if the experimental 
error has been determined, the rule would be to double the error and 
subtract this sum from the highest variant. The remainder after 
subtraction would rep- 
resent the nitrogen 
content below which 
all strains could be dis- 
carded without danger 
of discarding a high- 
nitrogen strain. (The 
same method applies 
to the use of experi- 
mental error in select- 
ing for yield.) In the 
case illustrated in fig- 
ure 9, all strains ana- 
lyzing above 2.6 per 
cent must be selected 
best is not being; left. 



e 

&n a 






















\&6 , 


--_, 




r^l 


""■----___ 


1 








'—— . 


----- 




""--- 


"~— ~ 


pvS 


< 

$ /.0 




















d 


\ 

X 























/234-567B9/0 

Fig. 9. — Diagram showing the method of selection for nitrogen con- 
tent when the experimental error is known. 



for further test to be sure that one of the 
If the experimental error equals one-half the 

real variations in strains compared, then no selection can be made, 

but all the strains must be re tested. 

SUMMARY. ^ 

(1) Wheat plants growing under field conditions or nursery con- 
ditions show great variation in nitrogen content. This variation, 
however, does not seem to be inherited but is apparently due to local 
variation in environment and is therefore not capable of transmission. 

(2) Centgeners, rows, and small plats vary almost as much as 
individual plants, owing to local variation in environment. 

(3) The most practical way of overcoming this variation is by 
replicating the plats a sufficient number of times to reduce the error 
to less than one-half the real variation. 

269 



32 



EXPERIMENTS IN WHEAT BREEDING. 



(4) To bring the experimental error within proper bounds, single 
plants should be repeated 4/) or more times, 16-foot rows 5 to 10 
times, and blocks 5.5 feet square 8 to 16 times. No data are given 
for centgeners, but the variation in centgeners is about the same as 
in the blocks. 

(5) In order to eliminate the undesirable strains, the experimental 
error must be less than one-half the real or expected variation. 

(6) The easiest and most practical method of growing strains to 
compare for nitrogen content is to plant in rows 12 to 16 feet in 
length and repeat 10 times in different parts of the field. Several 
series of check plats should a(lso be inserted. 

269 



II— EXPERIMENTAL ERROR IN THE NURSERY AND 
VARIATION IN: YIELD 



INTRODUCTION. 

A very large share of cereal breeding to-day consists in the separa- 
tion of pure strains from what we call our ordinary varieties of 
cereals. In dealing with new hybrids the separation involves the 
selection of the most desirable strains after types have been fixed. 
We are mainly concerned for the present in finding the best-yielding 
strains. This necessitates the finding of a method by which com- 
parative field tests can be made rapidly in large numbers. 

The method of comparing strains in "centgeners" first came into 
general use some 10 years ago, and later the "row" method was 
evolved. At present the Nebraska Agricultural Experiment Station 
is experimenting with a small block similar in size to the centgener, 
but sown at the ordinary rate of seeding. 

A number of sources of error in all these methods are due to unex- 
pected variations in soil and climate. It is the purpose of this paper 
to discuss some of these sources of error and to suggest methods of 
correction. 

VARIATION IN YIELD FROM CHECK ROWS. 

In our row-breeding work we use every fifth row as a check plat. 
All check plats are from the same seed and sown in the same way. 
A great variation is found in these check rows even when conditions 
appear quite uniform. Table XII shows the yield of 47 consecutive 
check rows in one of the 1909 series. These rows were 14 feet long 
and each was hand planted with 400 seeds of Turkey wheat. They 
were not quite as uniform as we sometimes have them, owing to dry 
weather in the spring, although the appearance of the plats was 
uniform enough at harvest time. One object in presenting the data 
here, however, is to illustrate the effect of repeating check plats on 
correction of error. All things being equal, the yields of the 47 plats 
should have been the same. But all factors can never be equal, so in 
row-breeding work, owing to unequal environment, we must expect 
a wide degree of error. The only practical way so far suggested to 
overcome this error is to repeat the plats, according to some sys- 
tematic method, enough times to equalize variations in soil or 
climatic effects. If the plats are repeated only a few times there is 
269 33 



34 



EXPERIMENTS IN WHEAT BREEDING. 



still danger of a large error due to the chance combination of plats 
unduly high or low. This is illustrated by data given in the lower 
half of Table XII, where all the above check rows have been brought 
together in groups of six each (except group Ti), taking every eighth 
plat to form a group, to show the chance of error in repeating a series 
of strains six times. 

Table XII. — Yield of 47 14-foot check plats of Turkey wheat in 1909. 
Check Plats in Consecutive Order. 



Grams. 


Grams. 


Grams. 


Grams. 


Grams. 


Grams. 


Grams. 


Grams. 


205 


239 


162 


165 


182 


205 


216 


230 


170 


240 


204 


279 


205 


270 


278 


310 


202 


167 


200 


238 


285 


265 


222 


238 


247 


216 


225 


284 


255 


265 


279 


155 


304 


272 


226 


237 


245 


150 


268 


186 


209 


310 


278 


347 


168 


306 


239 





Check Plats Systematically Repeated to Form Eight Groups. 



Group a. 


Group 6. 


Group c. 


Group d . 


Group e. 


Group/. 


Group g. 


Group h. 


Grams. 


Grams. 


Grams. 


Grams. 


Grams. 


Grams. 


Grams. 


Grams. 


205 


170 


202 


247 


304 


209 


239 


240 


167 


216 


272 


310 


162 


204 


200 


225 


226 


278 


165 


280 


238 


284 


237 


347 


182 


265 


285 


255 


245 


168 


205 


270 


265 


265 


150 


306 


216 


278 


222 


280 


268 


239 


230 


310 


238 


155 


186 






219 


239 


217 


285 


234 


216 


215 


272 



Groups arranged in order of average yield of included plats: g, 215; /, 21G; c, 217; 
a, 219; e, 234; b, 239; h, 272; d, 285. Average, 237. 

Groups a and d illustrate the chance grouping of high-yielding and 
low-yielding plats. With only 5 plats out of the 47 yielding above 
300 grams, three of them by chance fell into group d while a r num- 
ber below normal fell into group a. The average yields of the 8 
groups varied from 215 grams to 285 grams. This variation indi- 
cates the amount of experimental error to be expected under similar 
conditions. Since the experimental error is larger than the real 
variation expected in different strains of wheat, results obtained 
under such circumstances would not be reliable. Until our system of 
testing will show actual differences of 10 per cent in yield, it can not 
be of much value in comparing the yielding value of different strains. 

VARIATION IN YIELD FROM REPEATED ROWS. 

In order to make a more careful test of the accuracy of replicating 
row tests, 100 rows of Kherson oats were planted, each row being 
12.5 feet in length and containing 500 seeds. The plat chosen for this 
test was quite uniform and the appearance of the plat at harvest was 
very satisfactory. Three-fourths of the rows yielded from 225 to 275 
grams each, with a few much higher and a few very low. Table 
XIII shows these rows arranged hi consecutive order as they were 

269 



EXPERIMENTAL ERROR AND VARIATION IN YIELD. 



35 



in the nursery, with the yield of each row and the average yield of 
groups of five adjacent rows. 

We may get some idea of how replication corrects error by assem- 
bling these rows into series as in the comparative test of strains. 
These data are shown and also summarized in Table XIII. In series 
1 the yields of 5 adjacent rows are averaged (as rows 1 to 5, 6 to 10, 
etc.). In series 2 every twentieth row is taken (as rows 1-21-41-61- 
81, etc.) and averaged. In series 3 every tenth row is taken, making 
10 repetitions; and in series 4 every fifth row, making 20 repetitions. 

Table XIII. — Yield of thrashed grain from 100 rows of Kherson oats. 
By Rows and Groups of Five Adjacent Rows in Consecutive Order. 





Yield of grain . 




Yield of grain. 




Yield of grain. 




Yield of grain. 


Row 
No. 




Row 

No. 




Row 

No. 




Row 
No. 




Actual. 


Mean of 
5 rows. 


Actual 1 Mean of 
Actual. 5 rowg 


Actual. 


Mean of 
5 rows. 


Actual. 


Mean of 

.5 rows. 




Grams. 


Grams. 




Grams. ! Grams. 




Grams. 


Grams. 




Grams. 


Grams. 


1 


228 


] 


26 


252 




51 


244 


■. 


76 


233 


| 


2 


273 




27 


248 




52 


261 




77 


247 




3 


255 


} 236 


28 


206 


[ 246 


53 


258 


} 2.50 


78 


211 


} 225 


4 


224 




29 


2S0 




54 


244 




79 


237 




5 


204 


J 


30 


247, 




55 


245 


J 


80 


200 




6 


205 


1 


31 


2.57 




56 


248 


1 


si 


248 


l 


7 


230 




32 


240 




57 


229 




82 


200 




8 


260 


I 224 


33 


233 


| 235 


58 


211 


\ 221 


83 


227 


} 222 


9 


195 




34 


230 




59 


227 




84 


220 




10 


233 


J 


35 


217 




60 


188 




85 


214 




11 


257 


1 


36 


226 




61 


248 




86 


1S4 


l 


12 


243 




37 


190 




62 


257 




87 


233 




13 


250 


\ 248 


38 


222 


[ 220 


63 


270 


\ 263 


88 


244 


[ 234 


14 


230 




39 


261 




64 


264 




89 


241 




15 


261 




40 


200 




65 


275 




90 


270 




16 


235 


| 


41 


246 




66 


300 


1 


91 


241 


1 


17 


273 




42 


249 




67 


151 




92 


174 




18 


273 


\ 255 


43 


276 


I 254 


68 


153 


\ 216 


93 


247 


\ 242 


19 


263 




44 


237 




69 


205 




94 


266 




20 


230 




45 


261 




70 


272 




95 


281 


1 


21 


244 


1 


46 


267 




71 


194 




96 


240 


) 


22 


245 




47 


259 




72 


274 




97 


232 




23 


209 


\ 234 


48 


252 


\ 249 


73 


242 


\ 235 


98 


228 


247 


24 


247 




49 


251 




74 


235 




99 


290 




25 


224 


J 


50 


218 J 




75 


229 


J 


100 


245 


1 



Systematically Grouped in Various Ways to Show Effect of Replication on Reduction of Varia- 
tion in Yiele. 



Series 1. — Groups of 5 adjacent 
rows. 


Series 2.— Groups of 5 rows, tak- 
ing every 20th row. 


Series 3.— 

Groups of 10 

rows, taking 

every 10th row. 


Series 4.— 

Groups of 20 

rows, taking 

every 5th row. 


Yield. 


Devia- 
tion. 


Yield. 


Devia- 
tion. 


Yield. 


Devia- 
tion. 


Yield. 


Devia- 
tion. 


Yield. 


Devia- 
tion. 


Yield. 


Devia- 
tion. 


Grams. 
216 
220 
221 
222 
224 
225 
234 
234 
235 
235 


Grams. 
-21.8 
-17.8 
-16.8 
-15.8 
-13.8 
-12.8 

- 3.8 

- 3.8 

- 2.8 

- 2.8 

erage 


Grams. 
236 
242 
246 
247 
248 
249 
250 
254 
255 
263 


Grams 
- 1.8 
+ 4.2 
+ 8.2 
+ 9.2 
+ 10.2 
+ 11.2 
+ 12.2 
+ 16.2 
+ 17.2 
+25.2 


Grams. 
212 
223 
224 
229 
234 
234 
234 
236 
237 
238 


Grams. 
-25.8 
-14.8 
-13.8 

- 8.8 

- 3.8 

- 3.8 

- 3.8 

- 1.8 

- .8 
+ .2 


Grams. 
239 
231 
242 
242 
243 
246 
246 
248 
245 
256 


Grams. 
+ 1.2 
+ 3.2 
+ 4.2 
+ 4.2 
+ 5.2 
+ 8.2 
+ 8.2 
+ 10.2 
+ 17.2 
+ 18.2 


Grams. 
226 
229 
230 
237 
238 
239 
241 
243 
245 
250 


Grams. 
-11.8 

- 8.8 

- 7.8 

- .8 
+ .2 
+ 1.2 
+ 3.2 
+ 5.2 
+ 7.2 
+ 12.2 


Grams. 
234 
235 
238 
241 
241 


Grams. 
-3.8 
-2.S 
+ .2 
+3.2 
+3.2 


Av 


237.8 


11.4 






237.8 


7.9 


237.8 


5.8 


237.8 


2 6 













269 



36 



EXPERIMENTS IN WHEAT BREEPTNfl. 



Table XIII. — Yield of thrashed grain from 100 rows of Kherson oats — Continued. 
Summary Showing Comparison of Groupings. 



Number of rows in a group. 


Average deviation from 
mean yield when 
rows are — 


Coefficient of varia- 
bility when rows 
are- 


Variation of extremes 
in yield when rows 
are^- 




Adjacent. 


Distrib- 
uted. 


Adjacent. 


Distrib- 
uted. 


Adjacent. 


Distrib- 
uted. 


1 


Grams. 

21.26 

11.38 

7.60 

3.46 


Grams. 

21.26 

7.87 

5.84 

2.60 


Per cent. 
11.5 
5.50 
3.66 
1.56 


Per cent. 

11.5 

4.8 

3.0 

1.7 


Grams. 
151 to 300 
216 to 263 
227 to 251 
234 to 243 


Grams. 
151 to 300 




212 to 256 


10 


226 to 260 


20 


234 to 241 







There is less variation when the five rows are distributed through- 
out the plat than when adjacent; also the variation decreases as the 
number of repetitions increases. Evidently in the case under con- 
sideration it would be necessary to repeat about 20 times in order to 
obtain comparable data. 

To secure more data on this point, 500 row plats of Turkey wheat 
were planted in the autumn of 1909. The rows were each 16 feet in 
length, all planted uniformly and with the same seed in soil of average 
fertility and in good tilth. At harvest the rows appeared to be uni- 
form in character and would have yielded about 30 bushels to the 
acre. Table XIV summarizes the results. 

Table XIV. — Yield of grain from 500 16-foot rows of Turkey wheat, systematically 
repeated in various ways to show experimental error. 



Classification. 


Number 
of groups. 


Mean 
yield. 


Extreme 
variation. 


Average 
deviation. 


Standard 
deviation. 


Coeffi- 
cient of 
varia- 
bility. 




500 
f a 25 
1 b25 
1 c25 
I d25 


Grams. 
250. 7 
242.0 
256.0 
247.3 
256.6 


Grams. 
156 -403 
219. 6-277. 8 
233.6-281.4 
226. 4-272. 6 
228. 4-282. 4 


Grams. 
28.67 
13.3 
11.7 
11.9 
11.8 


Grams. 
35. 85 
15.76 
14.11 
13.03 
14.85 


Per cent. 
14.34 


Every 100th row, 5 rows in a group 


6.51 
5.51 
5.27 
5.79 




250.5 


227. 0-278. 5 


12.17 


14.44 


5.77 




1 a 25 
\ b25 




Every 50th row, 10 rows in a group 


245.1 
256.3 


224. 1-270. 7 
242. 0-276. 6 


10 

8 


12. 18 
9.69 


4.97 
3.78 




• 250. 7 


233. 0-273. 6 


9 


10.93 


4.37 




33 
25 




Every 33d row, 15 rows in a group 

Every 25th row, 20 rows in a group 


250.2 
250.7 


235. 5-273. 9 
234. 3-269. <> 


6.2 

7.4 


7.95 
9.28 


3.18 
3.70 



In this case the experimental error was much higher than with 
the 100 rows of oats (Table XIII) and did not reduce so rapidly by 
repetition. This may be due to the fact that the 500 rows of wheat 
covered a greater area than the 100 rows of oats, thus having more 
causes for variation. It is probable that the greater the number 
of strains to be compared the more replications will be necessary 

269 



EXPEKIMENTAL ERROR AND VARIATION IN YIELD. 



37 



because of the larger area they will cover. However, when repeated 
15 times, the average deviation is about half as much as when 
repeated 5 times, but replicating 20 times did not make a further 
improvement. It will be seen that the extreme variation is rather 
wide. It would be impossible to make a direct comparison of yield 
between strains or varieties tested under conditions where the 
variation of extremes is so large. It would be necessary in such 
case to select a rather large percentage of the high-yielding varieties 
and continue the test with them for some years. The method of 
selection will be hereafter explained. 



671 


657 

210 


703 

2M 


755 

2|£ 


760 

213 


686 

214 


592 

215 


739 

216 


732 

217 


710 

210 


753 

219 


680 

220 


680 

221 


677 

zzz 


795 

223 


723 

224 


658 

193 


713 

194 


613 

195 


632 

196 


667 

197 


645 


660 

199 


768 

ZOO 


786 

20I 


768 
aoz. 


666 

203 


843 

204 


795 
zos 


763 

ZOb 


716 

207 


74/ 

208 


657 

177 


671 

|78 


623 

179 


715 

160 


543 
isi 


613 
laz 


'640 

163 


798 

IS4 


750 

185 


76+ 

186 


995 

187 


793 

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936 

189 


755 

190 


792 

191 


838 

192. 


642 

161 


68 O 

162. 


654 

163 


673 

164 


760 

165 


709 

166 


682 

167 


7Z4 

168 


774 

169 


S60 

170 


787 

171 


725" 

172 


664 

173 


851 

174 


690 

175 


770 

176 


735 

145 


380 

146 


620 

14-7 


675 

I4g 


765 

149 


742 

ISO 


772 

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G98 

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652 

153 


661 

154 


768 

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777 

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745 

15 7 


768 

158 


851 

159 


719 

IbO 


SIS 

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598 

130 


705 

>3l 


642 

132 


704 

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643 

134 


650 

135 


572 

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752 

|37 


740 

138 


863 

139 


eeo 

IAO 


722 

141 


723 

142 


703 

143 


756 

144 


izn 
H3 


633 

ii4 


615 

M5 


116 


662 

117 


639 

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657 

119 


&oe 

120 


62.0 

121 


6 2,4 

122 


74-5 
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764 

124 


703 
125 


752 

126 


788 

127 


682 

128 


572 

97 


373 

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St>0 
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645 

too 


692 


644 

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632 

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574 

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606 

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806 

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791 

108 


629 

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&SO 

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679 

hi 


588 

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58o 

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4-25 

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732 

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730 

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706 

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732 

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736 

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655" 

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673 

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793 
9o 


765 

91 


576 

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609 
93 


568 

94 


728 

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620 
96 


see 

C5 


5Zb 

66 


506 

67 


777 


776 

69 


779 

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72/ 

71 


720 

72 


604 

73 


742 

74 


665 

75 


62/ 

76 


Gil 
m 


623 

78 


64fc 

79 


fe/7 

BO 


6)7 

49 


683 

SO 


726 

51 


835 

52 


663 
53 


664 

34 


691 
ss 


770 

56 


775 

57 


685 

5« 


723 

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583 

to 


580 

61 


395 

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511 
63 


653 

64 


602 

33 


662 

34 


640 

35 


700 

36 


650 


655 


563 

39 


60O 

40 


730 

41 


690 

42 


713 

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530 

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478 
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636 

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630 

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see 

2.0 


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25 


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at 


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zs 


560 
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so 


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2. 


790 

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597 

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632 


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535 


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495 

14 


6IS 

15" 


652 
16 



Fig. 10.— Diagram of plats of Turkey wheat, showing the arrangement of 224 blocks (each 5.5 feet square) 
and the yield of grain (in grams) for each block. 

VARIATION IN YIELD FROM SMALL BLOCKS. 

For this experiment 224 blocks, each 5.5 feet square, were laid 
out in a plat 14 blocks one way by 16 the other. The blocks were 
all sown to Turkey winter wheat in the fall of 1908. To sow these 
the drill, 5.5 feet wide, was driven straight across the first series of 
14 blocks, the boundaries of the blocks being later established. 
Each series was sown in the same way and no path or space was 
allowed between the blocks. Figure 10 is a diagram of the blocks, 
the yield in grams being marked in each block. A large variation 
in yield was found in the different blocks, amounting to 100 per 

269 



38 



EXPEKIMENTS IN WHEAT BREEDING. 



cent in the extreme cases, although the appearance at harvest time 
was fairly uniform. These plats have been combined in various 
ways in order to study the yields. The results are shown in 
Table XV. 

EFFECT OF REPETITION IN REDUCING ERROR. 

The first part of Table XV shows the 224 blocks combined in 
various ways, namely, 56 groups of 4 blocks each when every fifty- 
sixth block was taken, 28 groups of 8 blocks each when every 
twenty-eighth block was taken, and 14 groups of 16 blocks each 
when every fourteenth block was taken. The 56 groups of 4 blocks 
each were divided into 4 sets of 14 each and the 28 groups of 8 into 
2 sets of 14 each. This division into sets was for the purpose of 
having an equal number of blocks for comparison in each case. 
We find illustrations of a combination of high-yielding plats and 
low-yielding plats such as were noted in Table XII. For example, 



7*2 



$90 



748 



TPO 

































7. 


K 


7l> 


16 


74 


13 


6 \ 


13 


6i 


'8 


S. 


'8 


6\ 


•s 






























































■& 






























7- 


1-2 


e 


77 


7. 


?<? 


7C 


O 


61 


7° 


6 


r 8 


6 


TO 






























































































£1 


w 


e„ 


}3 


(, 


93 


e 


W 


7 


?9 


G. 


<7 


6 


'8 




























































































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(■ 


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c, 


W 


6 


0-/ 


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9/ 


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6 


S3 


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7. 


39 


7? 


>6 


7< 


12 


6' 


>/ 


6 


* 


6c 


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6. 


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6i. 


32 


6 


'3 


6 


57 


e, 


s 


6 


?4 


6 


TO 


6 


'7 



















































































































Fig. 11.— Diagrams of plats of Turkey wheat, showing the arrangement of 224 blocks (each 5.5 feet square) 
when combined in groups of adjacent blocks, with the average yield for each group: A, Groups of 4; B, 
groups of 8; C, groups of 10. 

when the blocks are repealed 4 times the range in yield varies from 
an average of 595.2 grams per block to an average of 786.5 grams 
per block, a difference of 32 per cent. If varieties were being tested 
by the same system, this variation would be more than we might 
expect in the yields of different kinds. 

When the blocks are repeated 8 times the average variation ranges 
from 627.5 to 717.8 grams, a difference of 90 grams, or 14 per cent. 
By repeating 16 times the extreme variation is reduced to 47 grams, 
or 7 per cent. However, with the exception of the extremes, the 
variation here is small. The question now to consider is the mini- 
mum number of blocks which will insure comparable results. If 
comparable results are to be secured the first season, the blocks 
should be repeated 15 to 20 times. If it were desirable to carry 
the strains for a period of 3 years, repeating 8 to 10 times would 
probably be sufficient, since this would give a total of 24 to 30 blocks 
for the 3 years. 

269 



EXPERIMENTAL ERROR AND VARIATION IN YIELD. 



39 



RELATION OF SIZE OF PLAT TO VARIATION. 

It is veiy desirable in plant-breeding work to determine the 
minimum size of plat that it is practicable to use, since with hundreds 
of strains to try each year it would be impossible to handle them 
in large plats. Taking the above series of 224 small blocks, the 
adjacent blocks could be combined to give a continuous series of 
larger and larger blocks. Figure 11 shows how these combinations 
were made and Table XV gives statistical results, showing also in a 
summary for two years the comparative effect of increasing the 
size of the bLock and of repeating small blocks. 



Table XV. 



Yield of Turkey wheat grown in 224 block plats (each 5.5 feet square) in 
1909 and 1910. 



Systematically Repeated to Form Groups of 4, 8, and 16 Blocks. 





g. 
S 
be 

B 


Season of 1909. 


Season of 1910. 


Classification. 


2 

a t, 
£ ft 


> . 

2 a 
B.2 
S3 


•a . 
a 

a> o 
bcfl 

> > 


"Ho 

"2.5 


OS 


2 

O u 


a. 2 


a 
» o 

g c3 

pv 

*4 


'O . 
■a o3 


1^ 


Every 56th block, 4 
blocks in a group. 


224 
f all 
J bl4 
1 c 14 
1 dl4 


680. 38 

66S. 82 
I ISO. (Hi 
680. 95 
683.36 


373 -995 
613. 25-721. 25 
645. 75-786. 50 
595. 25-728. 00 
627 -744. 75 


67. 23 
29.33 
32. 99 
21.71 
24.36 


81.98 
35.79 
39.80 
30.09 
32.09 


P.ct. 

13 

5.35 
5.77 
4.42 
4.69 


463.71 

468. 23 
467. 09 
450. 59 
468. 93 


300 -809 
441.75-502.75 
412. 25-504. 25 
3E7. 50-490. 50 
403.75-581.50 


47.62 
15.80 
15.36 
21.52 
35.12 


62.62 
17.88 
21.87 
26.34 
44.23 


P.ct. 

13.50 
3.82 
4.68 
5.84 
9.43 


Average 


680. 77 


620.32-745.12 


27.09 


34.44 


5.05 


463. 71 


413. 81-515. SO 


21.95 


27. 58 


5.94 




1 a 14 
\ bl4 


Every 28th block, 8 
blocks in a group. . 


674. 20 
686. 66 


627. 50-704. 88 
660. 38-717. 88 


18.04 
16. 45 


21.63 
18.62 


3.21 
2.71 


459. 41 
468. 01 


441. 3S-472. 50 
433.38-515.38 


8.46 
15.28 


9.65 
19.34 


2.10 
4.13 




680.43 


643.94-211.38 


17.25 


20.13 


2.96 


463.71 


437.38-493.94 


11.87 

6.47 


14.43 


3.11 




14 


Every 14th block, 16 
blocks in a group. . 


680. 43 


653. 25-700. 38 


7.24 


10.41 


1.53 


463. 72 


450. 86-490. 56 


9.60 


2.07 



Combined in Groups of 4, 8, and 16 Adjacent Blocks, to Show the Effect of Size of Plat on 

Variability. 



Four adjacent 
blocks in a group . 


f a 14 
1 b!4 
1 cl4 
I dl4 

/ a 14 
\ bl4 

14 


652 
681.48 

713.61 

676. 78 

680.97 


529. 75-725. 25 
617. 75-748. 25 
624. 50-825 
4S8.25-S01.50 


37. 36 
30. 84 
53.14 
70.96 


V.). OS 
35. 75 
61.46 
85.80 


7.53 
5.25 
S.47 
12.67 


443.18 
465. 30 
504.64 
441.71 


387. 25-497 
389. 50-576 
413.75-587.50 
386. 75-493. 25 


26.76 
45.62 
31.84 
26.37 


30.93 
33.86 
41.90 
31.49 


6.98 
11.57 
8.30 

7.13 


Average 


565.06-775.00 


48.07 


58.02 


8.48 


463.71 


394. 31-538. 44 


32.65 


39.34 


8.49 


Eight adjacent 
blocks in a group. . 


666 
695 


636. 13-S29 
586. 50-706. 75 


24.57 
55.93 


31.57 
70.30 


4.74 
10.11 


454. 21 
473. 18 


398. 62-510. 25 
S94. 12-545 


27.86 
31.55 


37.97 
40.01 


8.36 
8.45 


Average 


6S0 


611.31-767.87 


40.25 


50.93 


7.42 


463. 69 


396. 37-527. 62 


29.70 


38.99 


8.40 


Sixteen adjacent 
blocks in a group. . 


680 


603. 75-797. 06 


35.43 


48.87 


7.20 


463.71 


406. 69-509. 38 


21.67 


26.43 


5.70 



269 



40 



EXPERIMENTS IN WHEAT BREEDING. 



Table XV. — Yield of Turkey teheat grown in 224 block plats (each 5.5 jcct square) in 
1909 and 1910— Continued. 

Summary Based on this Average of Both Seasons, Showing the Effect on Coefficient of Vari- 
ability of Increasing the Size of Plat as Compared with Distributing the Same Area by a 
Systematic Method. 





Number of 

groups 
averaged. 


Coefficient of variability. 


Number of blocks combined in each group. 


Plats 

increased 

in size, 

blocks 

adjacent. 


Plats 
distributed 

systemati- 
cally. 


Four adja- 
cent blocks 
combined 
and combi- 
nation dis- 
tributed 4 
times=16 
blocks. 


1 


224 
56 
28 

14 


13.25 
8.48 
7.91 
6.45 


13.25 
5.44 
3.03 
1.80 


1 


4 




8 


\ 3.42 


16 


j 







Summary Based on the Yields of 1909, Arranged to Show the Relation Between Size of Plat and 

Average Deviation. 



Shape of plat. 



1 

lby 2 
lby 4 
2 by 2 
2 by 4 
lby 8 
2 by 8 
4 by 8 
7 by 8 



Number 
of blocks 
in plat. 



Total 
number 
of plats. 



224 
112 
56 
56 
28 
28 
14 



Average 
deviation. 



Per cent. 
9.76 
8.57 
7.16 
7.38 
6.05 
6.08 
5.30 
5.37 
5.29 



Average deviation when 
plats are made up by 
systematic method. 



Every- 



56th block. 

J2Xth block. 
14th block. 



Per cent. 



5.05 

2.96 
1.53 



Starting with a coefficient of variability of 13.25 per cent, it is 
decreased to 8.48 when the block is made 4 times as large, to 7.91 per 
cent when 8 times as large, and to 6.45 per cent when increased 16 
times in size. Table XV gives the result of repeating the same num- 
ber of plats equal distances apart. Here we see that where the plats 
are repeated 16 times the average variability for the two years rapidly 
decreases to 1.8 per cent. 

It might appear from a study of the first part of this table that if 
the size of the plat were constantly increased the variability would be 
constantly reduced. However, increasing the size of the plat beyond 
a certain point does not continue to remove the cause of variability, 
namely, variation in soil. The last part of the table, which contains 
the data for 1909, is arranged to show the effect of increasing the size 
of the plat. It indicates a rapid decrease in variability up to plats 
16 blocks in size, but no decrease in the next two cases. While acre 
plats are probably less variable than tenth-acre plats and tenth-acre 
plats less variable than hundredth-acre plats, yet plats of this size 
are too variable for direct comparison and they are much too large 

269 



EXPERIMENTAL ERROR AND VARIATION IN YIELD. 



41 



/909. 

Y/£~LQ /V/r/?06£W 

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coErnc/e/vr or t//i/?/^B/L/7-y. 



for practical plant-breeding work. On the other hand, repeating 
the plats in a systematic way constantly removes the Cause of varia- 
tion as the number of repetitions increases. It then appears that the 
most practical method of removing error is to repeat series of small 
blocks a rather large number of times. 

CONSTANCY OF VARIATION ON THE SAME PLATS. 

Table XV gives statistical data for 1909 and 1910 on the same 
blocks arranged in the same way both years. Figure 12 shows the 
average yield of each section and the average percentage of nitrogen 
in the two years for 
sections a, b, c, and d. 
The yield per block 
varied about the same 
for the two years, be- 
ing highest in section c 
in both seasons. The 
variation in nitrogen 
was not as regular, 
section c being highest 
in nitrogen in 1909, 
while in 1910 there was 
a small but regular 
increase in nitrogen 
from d to a. The 
second part of figure 12 
shows the coefficient 
of variability in both 
yield and percentage 
of nitrogen when the 
small blocks are com- 
bined in sets of four 
(Table XV). Section 
a was highest in varia- 
bility of both yield and nitrogen content in 1909 and low in 1910. 
Section 6 was low in variation in yield in 1909 and high in 1910. 
This would indicate that different seasons do not affect equally all 
parts of the plat, and illustrates the difficulty of "standardizing" 
plats by the system of sowing all plats to one crop for a season in 
order to determine relative yield. 

VARIATION IN YIELDS FROM CENTGENER PLATS. 

The centgener method consists of planting 100 plants in a centgener, 
6 inches apart each way, making blocks 5 feet square. In 1908, 178 
centgener blocks were compared for variability with an equal number 

269 



pert cs/vr P£/?c£/vr P£/?ce^t 


P£tfCfA/K 






L/2LjC3' 2 '£,£- ^ r (-1 


t-^Ur > 


fitTirr *.f.<Ji 7 > XT 


J. 7TT [ 











-Lt-^±~Z l-CWi- St-CtAt- 


'3-/&3 ? 


-tr.^r -jYcfcF- ZKyO 


L.X^r [ 











^~ >LC O 'It- J-t-A'^,f- 


P-'PJS 


iTZk7 ,Z «.£ fi7iD? 


4**11 




±— 






"7-CSl. "2-iZll £.'X$sk 


3~^t \ 


/.OC iV.tM- Z.Kt.70 


«7v? f 




I 



a 



w 



ya 



Fig. 12.— Diagrams showing Turkey wheat grown in 224 blocks, 
combined in four groups (Table XV, a, b, c, d) of 56 adjacent 
blocks to show variations in yield and nitrogen content in 1909 
pud 1910. 



42 EXPERIMENTS IN WHEAT BREEDING. 

of duplicate row plats 16 feet in length. The variability was found 
to be practically the same. Other data confirm this conclusion, 
although under unfavorable conditions centgener plats are quite 
variable, owing to the fact that the individual plants are so far apart 
that the missing plants are not compensated for by the tillering of 
neighbors, as is the case where the planting is at the normal rate. 

ALTERNATING CHECK ROWS AS A MEANS OF OBTAINING COM- 
PARATIVE YIELDS. 

In order to test the value of the method of alternating check rows, 
the 500 rows before referred to (pp. 36-37) were used as a basis for 
data. It was assumed that every odd-numbered row would repre- 
sent a check row, while every even-numbered row would represent a 
strain being compared with a check row. Thus, row No. 2 would be 
considered a strain to compare with rows 1 and 3 as checks. It is 
apparent from data heretofore presented that the error would be too 
great if only a single row were compared with its adjacent checks. 
For example, there are numerous cases in the 500-row plats where the 
even-numbered row would be 20 to 30 per cent higher or lower in 
yield than the average of the adjacent odd-numbered row plats. 
Table XVI shows the result of averaging five odd rows and the 
adjacent five even rows, i. e., rows 1, 3, 5, 7, and 9 are averaged to 
compare with rows 2, 4, 6, 8, and 10. In the first 10 rows, for example, 
the five odd rows averaged 235.6 grams per row and the five even 
rows 226.4 grams per row, or 9.2 grams less than their checks. In 
the next block the even rows yielded 9 grams more than the checks. 
Out of the 50 cases here cited the extremes vary from —26.6 to 
+ 32.8, with an average deviation of 10.14 grams or 4 per cent. In 
selective work it is the unusually high variants that are sought after, 
but with an experimental error greater than the expected variation 
they would be difficult to locate. Table XVI also shows the result 
of dividing the 500 rows into blocks of 20 and 40 rows and comparing 
the yield of odd and even rows in each case. While in most cases the 
average deviation is small, yet there are a number of quite wide 
variations. For example, when 50 series of five odd rows are com- 
pared with five even rows, 17 series, or about one-third, show a 
deviation greater than 5 per cent of the mean; when 25 series of 10 
odd rows are compared with 10 even rows, 6 series, or about one- 
fourth, show greater than 5 per cent average deviation; and when 
12 series of 20 odd rows are compared with 20 even rows, none show 
5 per cent deviation. 

EFFECT OF INCREASING LENGTH OF ROW. 

To increase the length of the row will decrease the error in about 
the same way as to increase the size of the block. In the 500-row 
plats just discussed most of the rows were in series and end to end, 

269 



Bui. 269, Bureau of Plant Industry, U. S. Dept. of Agriculture. 



Plate I. 



- 



Fig. 1 .— Head-to-Row Nursery, in which 25 Grains from a Single Head are 
Planted in a Row 20 Inches Long. 

The second year the seed from each 20-inch row is planted in a lG-foot row. 




Fig. 2.— Row-Plat Nursery, in which the Rows are 16 Feet in Length with 

a 4-Foot Alley Adjacent, thus Making the Beds 20 Feet in Width. 

These beds are slightly rounded, to give perfect drainage. 



Bui. 269, Bureau of Plant Industry, U. S. Dept. of Agriculture. 



Plate II. 



















- 


f.i 


%■, r ' j: "••"" 








IHBi- 



Fig. 1.— Increase Plats of One-Thirtieth Acre Each. 
Selected strains from the nursery are tested in these plats for 3 years. 




Fig. 2.— Increase Plats Harvested and Ready to Thrash. 
The plats in this field averaged 60 bushels per acre. 



EXPERIMENTAL ERROR AND VARIATION IN YIELD. 



43 



with only a narrow alley a few inches in width between the ends. 
By adding together the rows end to end, longer rows could be made. 
(PL I.) A total of 84 rows 64 feet in length was made in this man- 
ner, and the yields calculated. Table XVI gives the variability in 
the original 500 rows, each 16 feet long, in comparison with the same 
rows when combined into lengths of 64 feet. By increasing the 
length four times the deviation and variability are reduced not 
quite one-half. The longer rows are also less variable than blocks 
of five adjacent 16-foot rows, but more variable than five rows dis- 
tributed in a systematic way throughout the plat. 

The best length of row to use must be determined by circum- 
stances. If sufficient uniform land is available and it is more con- 
venient to make long rows, to do so would lessen the number of 
repetitions of plats necessary to reduce the error within proper 
limits, but it would always take a larger area to secure the same 
degree of accuracy with the long rows. 

Table XVI. — Yield, in grams, of Turkey wheat grown during the season of 1910 in 
500 rows, each 16 feet in length. 

Arranged by Odd and Even Rows and Averaged in Groups of Ten. 1 



Rows 1 to 100. 


Rows 101 to 200. 


Rows 201 to 300. 


Rows 301 to 400. 


Rows 401 to 500. 


Odd. 


Even. 


Differ- 
ence. 


Odd. 


Even. 


Differ- 
ence. 


Odd. 


Even. 


Differ- 
ence. 


Odd. 


Even. 


Differ- 
ence. 


Odd. 


Even. 


Differ- 
ence. 


205 


212 




246 


244 




258 


253 




259 


292 




27S 


230 




226 


222 




235 


298 




233 


241 




317 


340 




278 


238 




245 


231 




230 


245 




262 


219 




314 


285 




277 


280 




262 


238 




248 


226 




182 


220 




223 


219 




307 


300 




240 


229 


- 9.2 


266 


231 


3.8 


246 


239 


- 1.8 


238 


262 


9.4 


283 


295 




235.6 


226. 4 


245 


24S.8 


236.2 


234.4 


270.2 


279.6 


284.6 


278.6 


- 6 


180 


183 


228 


226 


224 


218 


198 


223 


268 


250 




214 


255 




242 


266 




222 


261 




251 


287 




258 


250 




256 


220 




220 


227 




256 


231 




223 


204 




253 


250 




216 


234 




213 


235 




229 


241 




209 


223 




242 


239 




237 


256 


9 


225 


245 


14.2 


292 


198 


-14.2 


229 


194 


4.2 


189 


2S7 




220.6 


229.6 


225.6 


239. 8 


244.6 


230.4 


222 


226.2 


242 


255.2 


13.2 


214 


231 


271 


212 


235 


229 


216 


216 


284 


276 




235 


208 




235 


238 




235 


271 




222 


204 




200 


217 




284 


316 




247 


227 




235 


212 




245 


236 




316 


285 




275 


240 




247 


255 




221 


242 




231 


194 




194 


243 




272 


228 


-11.4 


267 


296 


- 7.8 


273 


269 


4.8 


200 


218 


- 9.2 


363 


343 




256 


244.6 


253.4 


245.6 


239. 8 


244.6 


222.8 


213.6 


271.4 


272.8 


1.4 


272 


239 


269 


259 


219 


255 


228 


200 


248 


294 




275 


215 




250 


289 




270 


280 




227 


228 




380 


338 




224 


237 




278 


246 




275 


191 




218 


208 




326 


287 




220 


240 




222 


256 




282 


249 




242 


257 




265 


315 




182 


263 


4.2 


308 


276 


- .2 


268 


237 


-20.4 


221 


230 


- 2.6 


314 


290 




234.6 


238.8 


265.4 


265.2 


262.8 


242.1 


227.2 


224.6 


306.6 


304.8 


- 1.8 


156 


252 


297 


280 


213 


246 


215 


252 


328 


273 




227 


263 




230 


310 




255 


269 




269 


210 




324 


315 




254 


224 




323 


263 




235 


242 




171 


228 




300 


279 




226 


188 




317 


261 




247 


268 




230 


207 




252 


240 




246 


255 


14.6 


305 


268 


-18 


303 


242 


2.8 


222 


200 


— "2 


331 


273 




221. 8 


236.4 


294.4 


276.4 


250. 6 


253.4 


221.4 


219.4 


307 


277.8 


-29.2 



Average difference in yield between odd and even rows, grams, 10.4; per cent, 4. 



269 



44 



EXPERIMENTS IN WHEAT BREEDING. 



Table XVI. — Yield, in grams, of Turkey wheat grown during the season of 1910 in 
500 rows, each 16 feet in length — Continued. 
Arranged by Odd and Even Rows and Averaged in Groups of Ten— Continued. 



Rows 1 to 100. 


Rows 101 to 200. 


Rows 201 to 300. 


Rows 301 to 400. 


Rows 401 to 500. 


Odd. 


Even. 


Differ- 
ence. 


Odd. 


Even. 


Differ- 
ence. 


Odd. 


Kven. differ- 
ence. 


Odd. 


Even. ' Differ - 
ence. 


Odd. 


Kven. 


Differ- 
ence. 


227 


247 




275 


249 




257 


225 




282 


246 




224 


303 




230 


285 




241 


269 




190 


204 




269 


240 




349 


320 




263 


281 




285 


245 




227 


250 




250 


230 




272 


283 




255 


255 




249 


222 




222 


174 




233 


268 




291 


331 




280 


280 


18.6 


246 


223 


-17.6 


208 


216 


- 7 


213 
249. 1 


200 

236. N 


-12.6 


208 


271 




251 


269.6 


259.2 


241.6 


220.8 


213.8 


268. S 


301.6 


32. 8 


275 


237 


232 


228 


229 


187 


200 


207 


269 


293 




264 


277 




200 


228 




200 


215 




219 


233 




293 


327 




268 


227 




282 


242 




238 


238 




225 


207 




257 


263 




204 


218 




227 


239 




242 


202 




205 


230 




254 


244 




237 


202 


-17.4 


246 ' 


222 


- 5.6 


190 


245 


- 6.4 


243 


216 


.2 


250 


311 




249.6 


232.2 


237.4 


231.8 


223.8 


217.4 


218.4 


218.6 


264.6 


287.6 


23 


235 


229 


266 


287 


218 


212 


250 


208 


286 


243 




204 


210 




351 


312 




212 


184 




276 


254 




297 


403 




257 


312 




265 


300 




234 


267 




235 


245 




316 


285 




294 


295 




322 


313 




211 


213 




243 


255 




297 


239 




313 


315 


11.6 


293 


285 





232 


284 


10.6 


257 
252.2 


281 
248.6 


- 3.6 


211 


247 




260.6 


272.2 


299.4 


299.4 


221.4 


232 


281.4 


283. 4 


2 


233 


265 


248 


273 


230 


219 


298 


316 


208 


219 




276 


214 




233 


243 




236 


228 




261 


208 




255 


255 




327 


300 




280 


261 




290 


314 




225 


24S 




243 


289 




312 


316 




259 


263 




208 


195 




233 


226 




247 


275 




370 


290 


-26.6 


248 


272 


8.8 


225 


219 


- 2.8 


205 


214 


_ 2 


249 


266 




303.6 


277 


253.6 


262.4 


237.8 


235 


244.4 


242.4 


240.4 


260.8 


20.4 


271 


236 


241 


250 


232 


211 


250 


230 


217 


215 




251 


246 




266 


254 




185 


257 




254 


211 




235 


285 




269 


251 




310 


263 




242 


242 




205 


269 




252 


235 




217 


242 




245 


245 




279 


270 




237 


216 




222 


289 




298 


308 


- 4.6 


275 


269 


—11.2 


265 


270 


9.4 


242 


192 


-14 


271 


288 




261.2 


256.6 


267.4 


256.2 


240.6 


250 


237.6 


223.6 


239.4 


262.4 


23 



Summary of Odd and Even Rows Arranged in Blocks of 20 and 40 Rows to Show Deviation. 













The 20 odd and 20 even rows from 


The 10 odd and 10 even rows from each adjacent 20 grouped together. 


each adjacent 40 


grouped to- 












gether. 




Odd. 


Even. 


Difference. 


Odd. 


Even. 


Difference. 


Odd. 


Even. 


Difference. 


228.1 


228.0 


- 0.1 


222.6 


224. 7 


+ 2.1 


236.7 


234.8 


- 1.9 


245.3 


241.7 


- 3.6 


239.2 


242. 5 


+ 3.3 


245.7 


252.6 


+ 6.9 


236.4 


253.0 


+ 16.6 


246.1 


252.9 


+ 6.8 


25S. 8 


255.5 


-3.3 


255. 1 


252.2 


- 2.9 


225.0 


219.1 


- 5.9 


268.1 


257. 2 


-10.9 


282. 4 


266.8 


-15.6 


235.4 


228.1 


- 7.3 


264.4 


263.9 


— . 


235.3 


244. 3 


+ 9.0 


235.3 


233. 6 


- 1.7 


245.8 


237.9 


- 7.9 


259.4 


255. 4 


- 4.0 


241.0 


233.0 


- 8.0 


229.1 


229.1 





276. 8 


259.0 


-17.8 


263.3 


266.9 


+ 3.6 


242.6 


247.7 


+ 5.1 


268.4 


268.6 


+ .2 


271.0 


288.8 


+ 17.8 


230. 2 


223. 6 


- 6.6 


260.5 


259.3 


- 1.2 


287.9 


289. 7 


+ 1.8 


238. 1 


233.3 


- 4.8 


240.4 


232.4 


- 8.0 


273.0 


285. 5 


+ 12.5 


267.1 


277.8 


+ 10.7 


251.3 


243.5 


- 7.8 


239.9 


261.6 


+21.7 


280.4 


287.6 


+ 7.2 


235.7 


233. 6 


- 2.1 




















Average difference. 


7.256 


Average difference. 


5.483 



Summary Showing Result of Combining 16-Foot Rows in Various Ways. 



Classification. 


Extreme 
varia- 
tion. 


Standard 
devia- 
tion. 


Coeffi- 
cient of 
variabil- 
ity. 


Classification. 


Extreme 
varia- 
tion. 


Standard 
devia- 
tion. 


Coeffi- 
cient of 
variabil- 
ity. 


500 single rows 16 feet 


156-103 
196-284 


35.85 

21.43 


Per cent. 
14.33 

8.8 


5 adjacent rows 16 


212-317 
227-278 


26.11 
14.44 


Per cent. 
10.38 


84 rows 64 feet long 
(4 times length of 


5 rows 16 feet long 
distributed (ev- 
ery 100 rows) 


5.77 







269 



EXPERIMENTAL ERROR AND VARIATION IN YIELD. 



45 



Table XVII shows a comparative summary, based on the data 
herein reviewed, from which it appears that to repeat the 5.5-foot 
square blocks, in series, will reduce the error at the greatest rate, 
while to repeat the 16-foot rows will give the next most rapid reduc- 
tion. However, the method of alternating 5 odd rows with 5 even 
rows gave about as good results as to repeat 10 rows, and the system 
of alternate planting with check rows would sometimes be desirable. 

Table XVII. — Summary shotving coefficients of variability under various systems of 
arranging block plats and row plats. , 



Kind of plats and 


Number of plats combined. 


Remarks. 


arrangemeni . 


1 


5 


10 


15 


20 


Blocks 5.5 feet square (Table 
XV):. 


13 
13 

14 

14 

14 


8 
5 

11 
5 


7 
2.5 

7 

4 
4 


6.4 
1.8 

5 

3.2 

3.6 


3.5 

3.7 
3 


Variation will not continue to 




decrease. 


Rows 16 feet long (Table 
XVI): 


Variation does not continue to 




decrease. 




Do. 







To correct by check plats is sometimes uncertain, as pointed out 
hereafter, and therefore the advantage seems to be with the method 
of systematic repetition of rows or blocks. The repetition of the 
square blocks 10 times gave a higher degree of accuracy than repeat- 
ing rows even 15 and 20 times, and it seems probable that further 
experimenting is likely to show the block system to be the most accu- 
rate for close comparisons. It also does away with the competition 
which no doubt takes place between adjacent rows, and also makes 
note taking easier by giving a mass effect, such as is secured under 
field conditions. To increase the size of plat will also reduce error, as 
shown by Table XV, and on the basis of these data a plat, about three 
times the size of the 5.5-foot blocks reported on, is being tested. This 
block is 4.2 by 16 feet in size, and indications are that with this block 
the variation will be reduced about one-half, as compared with the 
5.5-foot block. 

INFLUENCE OF RATE OF PLANTING ON YIELD. 

For several years in planting our row plats care was taken to plant 
the same number of seeds in each row. In case of wheat, 400 kernels 
usually were planted to the 16-foot row, which was equivalent to the 
normal rate of seeding, or 5 pecks per acre. However, in 1908 and 
1909 counts of the number of plants harvested were made of many 
rows at harvest time. In the row plats of wheat where the rate of 
seeding was about normal it was found that only about 60 to 80 plants 

269 



46 



EXPERIMENTS IN WHEAT BREEDING. 



were harvested to every 100 kernels planted. A variation of 20 per 
cent in stand was not apparent to the observer because all plats 
would appear to have an equally good stand at harvest time. This 
loss of plants was due to many causes, such as winterkilling, insects, 
and accidents, but chief among the causes appeared to be the normal 
competition of plants. For example, certain plants were weak or 
were slow in starting spring growth; the stronger plants would quickly 
outdistance them, causing at least a certain percentage of the weaker 
plants to perish as a result of competition. It seemed doubtful, how- 
ever, whether this difference in plants harvested had a marked effect 
on yield. For example, here and at many experiment stations tests 
have been made with sowing wheat at various rates, from 4 pecks to 
10 pecks per acre. The difference in yield is never large. Doubling 
the amount of seed sown, from 4 to 8 pecks per acre, does not double 
the yield, and in many cases does not affect it at all. This is due to 
the tillering power of the plant, which is able in this way to compen- 
sate for the difference in number of plants. 

To make a test of the rate of planting under row-plat conditions, a 
series of plats was planted with Red Rustproof oats in the spring of 
1910. Each row plat was 16 feet in length. There were 5 plats in the 
series, planted at the rate of 400, 500, 600, 700, and 800 grains per 
plat. The series was repeated 20 times, making 100 rows in all. The 
results are shown in Table XVIII. 



Table XVIII. — Results of r a te-of -seeding test on 100 16-foot rows of Red Rustproof oats. 



Statement < 


f averages. 




N umber of grains sown per row. 


400 


500 


600 


700 


800 




20 
197 


20 
213 


20 
215 


19 
215 


20 


Average yield per row 




grams.. 


234 



The normal rate of seeding would have been about 600 grains per 
row. It appears from the data that a slight variation in rate of 
planting, as 25 or 50 grains more or less than normal, would not 
affect the results. 

To further test the effect of rate of seeding, a series of 60 blocks 
was laid out, each block being 5 drill rows wide and 16 feet in length. 
As the drill rows were 10 inches apart, this made the plats each 4.2 by 
16 feet. The blocks were planted with a small drill devised for the 
puqjose. Five rates of seeding were used, namely, 42.6,' 49.1, 55.9, 
65.4, and 73.3 grams per block. The series was repeated 12 times, 
giving 12 blocks of each rate for averaging. The results are shown 
in Table XIX. 

269 



EXPEKIMENTAL ERROR AND VARIATION IN YIELD. 47 

Table XIX. — Results of rate-of-seeding test on 60 block plats of Kherson oats. 



Statement of averages. 


Weight of seed sown (grams). 


42.6 


49.1 


55.9 


65. 4 ; 73. 3 




12 
1,069 


12 

1,101 


12 
1,151 


12 12 






1,149 1 1,156 



The normal rate of seeding would be about 60 grams per block, and 
it is apparent from the data that a variation of 10 or even 20 per cent 
above or below normal in the weight of seed used would not have a 
marked effect on the yield. 

In view of the data just presented, it would seem not to be necessary 
to actually count the number of seeds to be planted in each small plat, 
providing some other quicker means can be found of obtaining 
approximate accuracy. If the seed is first carefully fanned, scoured, 
and screened to one size, equal volumes will usually not vary more 
than a small percentage in number of kernels^^AIso equal weights 
will have approximately the same number of kernels, provided the 
seed has first been carefully prepared by fanning and screening to a 
uniform size. 

EFFECT OF COMPETITION BETWEEN ADJACENT ROWS. 

In 1908 it was observed that a certain strain of early wheat in a 
series of row plats made a very poor appearance at harvest time, 
while the same strain planted in centgeners made a much better 
comparative showing. Apparently the larger and faster growing 
strains on each side, the rows being only 8 inches apart, exercised 
some competitive effect. This effect of competition has been noted 
for two years since. Also in certain variety tests of oats, grown in 
row plats 10 inches apart, the same effect was noted. Exact data 
can not be given on this point, as the results from the series of plats 
planted in 1909 and in 1910 for this purpose were seriously impaired 
by unfavorable conditions; but Table XVIII, giving results from 
adjacent row plats sown at different rates, shows that the 800-seed 
rate made a marked increase over the 700-seed rate, while in a similar 
series of blocks (Table XIX), sown at the same rate, this marked 
increase was not noted. Since the 800-seed row was always adjacent 
to the 400-seed row, it may have had some advantage on this account. 
Danger from this source can probably be avoided if care is taken to 
plant only similar varieties in adjacent rows. Where the block plat 
is used this source of error is eliminated. 

269 



48 



EXPERIMENTS IN WHEAT BREEDING. 



VARIATION IN PURE STRAINS AND RELATION OF DATA IN 
CENTGENER NURSERY AND IN FIELD PLATS 

ISOLATION OF PURE STRAINS. 

In 1902, Dr. T. L. Lyon, now of Cornell University, planted 800 
heads of Turkey winter wheat in a centgener nursery, arranging to 
keep a record of the progeny of each head. The heads were num- 
bered from 1 to 800 and these original numbers are still retained as 
family numbers. The original plan was to select for increased 
nitrogen content and yield, discarding those families which did not 
show high averages in both these respects, and to practice con- 
tinuous selection of individual plants from among those families 
that were promising. A considerable number of the families were 
discarded each year, until at the end of harvest in 1906 only 47 of 
the original 800 were retained for further work. At this time the 
writer took up the work and the practice of continuous selection was 
discontinued as it began to be apparent that the isolation of pure 
strains was a more promising way of obtaining results. The 47 
pure strains were put in field plats to test for yield. Complete 
records, however, can be given on only 24 pure strains, as all but 26 
were dropped in 1908 for lack of space, and the nursery data are 
incomplete on 2 strains out of the 26. These strains are shown in 
field plats in Plate II. Table XX gives the average results for four 
years, both in the centgener nursery and in the field plats. By 
"centgener" is meant the method of planting 100 seeds from a single 
plant in a square plat, the plants 6 inches apart each way. 

Table XX. — Relations of certain characters of 24 strains of Turkey wheat grown in 
nursery and in field and tested during 4-year periods. 

Ranked in Groups of Five in Order of Yield in the Field. 



Data from centgener nursery (average for four vears, 
1906-1909). 



Family No. 

(The numbersinitalicindieate 
the five highest yielders.) 



Total or average. 



556. 
225. 
215. 
47.. 



/'. ct. 

2.66 
2.52 
2.68 
2.61 
2.70 



2.63 



2.72 
2.53 
2.63 
2.60 
2.70 



Yield per- 



Grams. 
13. 38 
12.38 
11.58 
12.27 
9.83 



11.89 



12.36 
11.12 
11.14 
12.26 
11.01 



P ~ 



Gins. 
764 
704 
622 
646 
612 



670 



593 
623 
605 
664 
620 



*2 



Grams. 

0. 02192 
. 01864 
. 02105 
. 02344 
. 01824 



. 02058 



. 02267 
.01984 
. 02064 
. 02013 
. 02168 



/■. a. 

80 
81 
63 

68 
67 



72 



Days. 
36 
35 
35 
36 
35 



35 



Data from field plats 
(average for four 
vears, 1907-1910). " 



P. ct. 
2.60 
2.49 
2.48 
2.55 
2.56 



134 



38 
29 
48 
123 
18 



2.54 



2.54 
2.55 
2.54 
2.51 
2.53 



Bush. 
40. 7.5 
40.59 
39.90 
39.21 
39.18 



39.93 



38.86 
38.78 
38.64 
38.50 
38.48 



>tal or average 2.64 11.58 621 .02099 63 35 256 2.53 

1 Averages of check plats: Nitrogen content, 2.61 per cent; yield. 35.18 bushels 
269 



38.65 



EXPERIMENTAL ERROR AND VARIATION IN YIELD. 



49 



Table XX. — Relations of certain characters of 24 strains of Turkey wTieat grown in 

nursery and infield and tested during 4-year ■periods — Continued. 

Ranked in Groups of Five in Order of Yield in the Field— Continued. 





Family No. 

numbers in italic indicate 
e Ave highest yielders.) 


Data from centgener nurserv (average for four years, 
1906-1909). 


Data from field plats 
(average for four 
years, 1907-1910). 




G 
g 

a 
o 
o 

CI 
0) 
BO 

o 
u, 

% 


Yield per — 


o 

+J OS 

a <d 
>- G 
> a> 


i 

O 

bo 

G 

s 


■d 

_o 
'C 

CO 

P, 

so 
g 

! 


G 
a 

u . 

o o 

I- > 
■9 « 

G *-< 

s * 


a 
3 

a 

o 
o 

a 

s 
2 


2 


5 

Pi 


(The 
th 




5 00 

JfJ. 

f- cr. 

O i-H 

O 


•a 

O M 

a> > 


391 


P.ct. 
2.70 
2.63 
2.50 
2.81 
2.59 


Grams. 
10.93 
12.46 
11.95 
11.05 
11.08 


Gms. 
510 
647 
597 
563 
558 


Grams. 
. 02185 
. 02295 
.02118 
. 02016 
. 01889 


P. ct. 
64 
64 
68 
60 
65 


Days. 
34 
34 
36 
34 
34 


28 
59 
114 
20 
26 


P.ct. 

2.51 
2.59 
2.53 
2.70 
2.58 


Push. 
37.96 
36.57 
36.27 
36. 13 
36.12 


5 


221 


12 


313 


5 


377 


5 


206.. - 


5 










2.65 


11.49 


575 


.02111 


64 


34 


247 


2.58 


36.61 


32 








314.. 


2.68 
2.63 
2.76 
2.84 
2.52 


9.70 
10.70 
10.03 
10.79 
12.11 


560 
512 
614 
620 
594 


. 02020 
. 02247 
. 02029 
. 02057 
. 02108 


66 
63 
66 
62 
66 


34 
34 
34 
24 
35 


52 
23 
18 
20 
43 


2.63 
2.60 
2.73 
2.71 
2.48 


35.22 
34.84 
34.20 
33.56 
33.46 


8 


108 


8 


526 


5 


379 





216. 


8 










2.69 


10.67 


580 


. 02089 


65 


34 


156 


2.63 


34.26 


34 








20'.).. 


2.49 
2.87 
2.56 
2.62 


11.38 
11.27 
9.S6 
11.89 


570 
526 
548 
508 


.01915 
. 02270 
. 02180 
. 02522 


82 
54 
58 
62 


34 

34 
36 
33 


37 

48 
33 
30 


2.45 
2.75 
2.55 
2.73 


32.93 
32.58 
31.88 

28.88 


8 


37 


5 


2 . 


8 


32S . . 


5 










2.63 


11.10 


538 


. 02228 


64 


34 


148 


2.62 


31.56 


26 











Summary of Results, Arranged in Groups of Five Strains and Ranked in Various Ways. 



CENTGENER TESTS. 

In order of nitrogen content: 

37,379,377,526,556 

^5,391,3,314,^ 

45,221,168,215,328 

SIS, 47, 206, 2, 225 

257,216,313,209 

In order of strength of straw: 

209,287,48,215,313 

313,425,314,526,216 

206,225,391,221,3 

42,168,47,379,328 

377,2,556,37 

In order of vield per plant: 

48, 221, 257,556, 312 

47,216,313,328,42 

209,37,215,225,206 

377,526,3,391,379 

168,2,425,314 

In order of vield per centgener 

48,287,47,221,312 

225,42,3,379,526 

425,215,313,216,556 

209,377,314,206,2 

37,168,391,328 

FIELD-PLAT TESTS. 

In order of nitrogen content: 

37, 526, 32S, 379, 377 

314,45,168,221,206 

425,2,225,3; 2, 556 

215,3,313,391,47 

257,42,216,209 

In order of yield per acre: 

48,287,42,312,425 

556,225,215,47,3 

391,221,313,377,206 

314,168,526,379,216 

209,37,2,328 

209 



2.80 


11.10 


583 


2.69 


10.61 


585 


2.63 


11.91 


607 


2.58 


11.32 


608 


2.51 


11.95 


616 


2.58 


12.11 


658 


2.63 


10.72 


595 


2.63 


11.32 


592 


2.67 


11.44 


585 


2.74 


11.13 


558 


2.63 


12.57 


671 


2.58 


11.96 


597 


2.62 


11.20 


576 


2.76 


10.76 


585 


2.64 


10.02 


558 


2.60 


12.55 


685 


2.70 


10. 91 


620 


2.61 


11.48 


600 


2.63 


10.61 


560 


2.70 


11.20 


514 


2.78 


11.01 


566 


2.64 


11.46 


608 


2.62 


11.09 


604 


2.63 


11.46 


604 


2.55 


11.86 


622 


2.63 


11.89 


670 


2.64 


11.58 


621 


2.65 


11.49 


575 


2.69 


10.67 


580 


2.63 


11.10 


538 



0. 02128 


59 


34 


144 


2.69 


35.07 


. 02060 


65 


34 


156 


2.54 


38.15 


. 02224 


68 


34 


182 


2.61 


35. 94 


. 02082 


64 


35 


242 


2.55 


36.90 


. 02001 


74 


35 


217 


2.49 


35.81 


. 02076 


76 


35 


161 


2.53 


38.42 


. 02020 


67 


35 


262 


2.59 


35.67 


. 02104 


64 


34 


160 


2.55 


37.58 


.02189 


63 


34 


219 


2.61 


35.14 


. 02183 


57 


35 


139 


2.63 


34. 86 


. 02192 


70 


35 


173 


2.55 


39.20 


.02173 


64 


35 


333 


2.55 


35.40 


. 02024 


67 


34 


188 


2.57 


35. 81 


. 02091 


63 


34 


104 


2.64 


36.07 


. 02068 


63 


35 


143 


2.58 


35.28 


. 02041 


71 


35 


258 


2.55 


39.12 


. 02068 


64 


34 


108 


2.60 


36.98 


. 02076 


65 


35 


278 


2.53 


37.28 


. 02040 


66 


34 


168 


2.58 


34.46 


. 02306 


61 


34 


129 


2.65 


33.56 


.02179 


61 


34 


136 


2.72 


33.07 


. 02129 


68 


34 


182 


2.60 


36.70 


.02120 


63 


36 


166 


2.55 


37.58 


.02120 


66 


35 


331 


2.52 


37.97 


.01998 


73 


35 


126 


2.47 


36.72 


.02058 


72 


35 


134 


2.54 


39.93 


. 02099 


63 


35 


256 


2.53 


38. 65 


.02111 


64 


34 


247 


2.58 


36.61 


. 02089 


65 


34 


156 


2.63 


34.26 


. 02228 


64 


34 


148 


2.62 


31.56 



50 



EXPERIMENTS IN WHEAT BREEDING. 



To sum up, the 24 pure strains have varied in the centgeners from 
2.49 to 2.87 in per cent of nitrogen, from 54 to 82 per cent in strength 
of straw, from 9.70 to 13.38 grams in yield per plant, and from 508 to 
764 grams in yield per centgener. They also have showi^ a variation 



, ■> 




Fig. 13.— Field plats of pure strains and check plats of original seed of Turkey wheat, 1910. The upper 
numerals are family numbers: the lower, 4-year average yields. Two of the poorest yielders out of 20 
strains came adjacent to two of the best. The difference in yield would not have been suspected from 
the appearance of the plats. 




Fig. 14.— Wheat nursery plats, showing variations in winterkilling. Pure strains were alternated with 
the original Turkey wheat from which the strains were isolated. The original was mostly winterkilled 
while many of the select strains withstood the winter well. 

in average weight of kernel ranging from 0.01824 to 0.02522 gram. In 
the field plats the percentage of nitrogen varied from 2.45 to 2.75 and 
the yield per acre from 28.8 to 40.7 bushels — -a difference of about 12 

269 



EXPERIMENTAL ERROR AND VARIATION IN YIELD. 



51 



bushels. Some of these plats and the check plats noted below are 
shown in figure 13. It is interesting to note that the check plats of 
original unselected Turkey winter wheat averaged 35.18 bushels per 
acre, or about halfway between the highest and lowest pure strains. 
More strains surpass the check in yield than fall below it, but this is 
probably because a large percentage of the poor-yielding strains were 
discarded after the first field test in 1907. It appears that neither the 
original selection of the 800 heads, nor the discarding of centgeners in 
the nursery, nor the continuous selection of high-yielding plants within 
the centgeners had any effect on eliminating the poor yielders. There 
was a marked difference in the appearance of the pure strains, some 




Fig. 1.5.— Field plats, showing variations in winterkilling between two pure strains of Turkey wheat. 
Strain No. 377 is shown at the right and No. 102 at the left; No. 377 withstood the winter almost perfectly. 

having short grains and others long grains. They also varied in color, 
lodging, and general appearance in the field, both in fall growth and 
spring growth. Figures 14, 15, 16, and 17 illustrate these variations 
better than they can be described. 

Table XX also shows the data from Table XV grouped in series 
of 5, and arranged hi various ways to illustrate relationships. The 
principal considerations in this work were the improvement of wheat 
in nitrogen and yield. Records were kept of many characters of the 
plant in the nursery, but evidence points to six that are of interest, 
namely, (1) nitrogen content, (2) yield per plant, (3) yield per cent- 
gener, (4) weight of kernel, (5) strength of straw, and (6) length of 
fruiting period. 

269 



52 



EXPERIMENTS IN WHEAT BREEDING. 



PERCENTAGE OF NITROGEN. 

The percentage of nitrogen is in inverse ratio to strength of straw 
and length of fruiting period, but has no direct relation to other char- 
acters. It is transmit ted in the field plats as indicated in the summary 
of Table XX. A striking example of this conclusion is seen in a com- 
parison of families Nos. 209 and 37, Table XX. These families represent 
the two extremes in percentage of nitrogen and strength of straw, with 
an inverse relation, but are nearly the same in all other characters. 

From 1903 to 1906, records were kept of individual plants selected 
from the nursery. When these plants were classified according to 




Fig. lG.— Increase rows of Turkey wheat, showing variations in the time of heading in different strains, 
each from a single plant. Four rows of each strain are grown. 

percentage of nitrogen or size of kernel, regardless of the family from 
which they came, there was a marked inverse relation, the percentage 
of nitrogen increasing as the size of kernel decreased. It seems prob- 
able, however, that the individual plants having small kernels may 
have suffered some degree of arrested development, since this relation 
disappears when the pure strains are so classified. Percentage of 
nitrogen and yield per acre in field plats vary inversely. 

STRENGTH OF STRAW. 

Strength of straw varies inversely with percentage of nitrogen and 
directly with yield per acre and yield per centgener. 

269 



Bui. 269, Bureau of Plant Industry, U. S. Dept. of Agriculture. 



Plate III. 







&JL iMmn^^ 






-. /Kq -■•j 




0M **'*' 


- 




PP*:"*" ':-■'"". 




HHBjjEJfljjffigfr^ScMBIfc 


msn 


BIWWrEB^^^S^^ 


SW^f?^i^^SjB 



Fig. 1.— Type of Road Grader or Drag Used in Grading a Nursery into Beds 
20 Feet Wide to Afford Uniform Drainage. 




Fig. 2.— Grains of Turkey Wheat, Showing Variation in Appearance. 

Nos. 51 and 60 are typical kernels from two pure strains and represent the shortest and longest 
kerneled types out of 80 strains. No. 76 is a hard, vitreous kernel, somewhat approaching 
the durum wheat in type. No. 75 is a soft wheat. The plants of this strain are typical Turkey 
in appearance but the grain is larger and almost white. Notwithstanding the white color, 
this strain was the highest in nitrogen content of 80 strains in 1910. 



Bui. 269, Bureau of Plant Industry, U. S. Dept. of Agriculture. 



Plate IV. 




Fig. 1.— Representative Kernels from 4 Strains of Turkey Wheat, Selected 
to Show Variation in Appearance. 

No 48 is a large plump-kerneled strain, while No. 287 has a rather small kernel. No. 328 has 
a large dark-colored kernel, while No. 313 hasa decided yellow color and is long and pointed. 




Fig. 2.— Representative Kernels from 4 Strains of Turkey Wheat, Selected 
from a Series of 80 Strains to Show Variation in Quality. 

On the basis of a perfect wheat, grading 100, these strains grade as follows: No. 77 grades 50, 
No. 51 grades 70, No. 27 grades 80, and No. 42 grades 95. 



EXPERIMENTAL ERROR AND VARIATION IN YIELD. 53 



YIELD PER PLANT. 



The yield per plant shows some correlation to yield per acre and 
yield per centgener, but this correlation is not high, as it is only in the 
first class that the correlation is marked. One of the best-yielding 
strains (No. 425) had a small plant yield in the nursery. 



YIELD PER CENTGENER. 



The yield per centgener shows a high correlation with yield per acre 
and strength of straw, but not a close relation to other characters. 



SIZE OF KERNEL. 



The size of kernel (PL III, fig. 2) appears to have no fixed relation- 
ships; as a character of a pure strain it seems to be independent of 
other characters. An example of this is shown in Table XX. Families 




Fig. 17.— Field plats of Turkey wheat, showing variations in stiffness of straw in two strains. Each strain 

originated from a single plant. 

Nos. 287 (PI. IV, fig. 1) and 425 have small kernels, but they are 
among the best in yield, while No. 328 (PL IV, fig. 1) is poorest in 
yield, but has the largest kernel. Nos. 48 and 287 are the best 
yielders out of the 26 strains (Table XX), averaging 40.7 and 40.6 
bushels per acre, respectively, in a four-year test. No. 48 has a large, 
plump kernel, while No. 287 has a rather small kernel. No. 328 has 
averaged 28.9 bushels under the same conditions, yet tins strahi has 
a large, dark-colored kernel. Our records do not seem to show a rela- 
tion between the appearance of the berry and the yield. No. 313 has 
averaged 36.3 bushels per acre, but the kernel has a decided yellow 
color, and is long and pointed in shape, approaching a rye grain in type. 

QUALITY OF KERNEL. 

As already noted, there does not seem to be a definite relation 
between the appearance of the berry and the yield of the strains. 

269 



54 



EXPERIMENTS IN WHEAT BEEEDING. 



Plate IV, figure 2, illustrates four strains of Turkey wheat selected 
from a series of eight strains to show variation in quality. On the 
basis of a perfect wheat grading 100 these strains grade as follows: 
No. 77 grades 50, No. 51 grades 70, No. 27 grades 80, and No. 42 
grades 95. These grades indicate the variation in quality found in 
pure strains and show the great possibility of improving quality 

(fig. 18). 

To sum up, high yield in the field is associated with high yield per 
centgener and strong straw, has a slight relation to size of plant, no 
relation to size of berry, and varies inversely with percentage of 




Fig. 18.— Cereal laboratory, showing the method of taking notes on quality. Comparisons of 80 strains 
of Turkey wheat are being made. There were 10 plats of each strain, making 800 in all, but the 10 samples 
of each strain are arranged together. Notes are taken on each sample separately, then an average is made 
of the results. To facilitate note taking, a set of "standard samples" representing different qualities is 
kept in long, 2-ounce vials. A set of these vials is plunged into the sample, and by comparison very 
accurate data are obtained. 

nitrogen. A high or a low nitrogen content as indicated in the nursery 
gives correlated results in the field. High nitrogen content is antag- 
onistic to high yield. However, an occasional strain, such as No. 48, 
combines a fair percentage of nitrogen with high yield. 

SUPERIORITY OF STRAIN. 



From the point of view of yield per acre there would seem to be 
little choice among the five best strains (Table XX), but in some 
ways No. 48 is outstanding in desirable qualities. With a high yield 



269 



EXPERIMENTAL ERROR AND VARIATION IN YIELD. 55 

per acre, it still is above the average in nitrogen content, has a strong 
straw and a large berry of good appearance. It is also very winter 
resistant, as was shown in the severe winter of 1909-10, when it 
came through with much less winterkilling than standard varieties, 
such as Big Frame and ordinary Turkey wheat. 

COMPARISON OF ROWS, CENTGENERS, BLOCKS, AND FIELD PLATS. 

In 1909-10 the 26 strains of Turkey wheat were sown in field plats 
and duplicated in rows, centgeners, and blocks, but this portion of 
the nursery was winterkilled. However, very good results were 
obtained with 11 varieties of oats sown in the spring of 1910 in all 
four ways. The field plats were one-fifteenth of an acre in size and 




Fig. 19.— Block nursery, showing blocks 4.2 by 16 feet in size. The beds are slightly elevated, as In the row 

nursery. 

were repeated three times. Each variety was repeated 10 times in 
centgeners, rows, and blocks. The centgeners were each 5 feet square 
and contained 100 plants 6 inches apart each way. The rows were 
12 feet in length and the grain sown in them at the rate of 10 pecks 
per acre, the usual rate of seeding in this region. The blocks were 
each 4.2 by 16 feet, or 5 drill rows wide (fig. 19), and sown at the 
usual rate of seeding. The results summarized in Table XXI show a 
high degree of correlation between the yield of the field plats and the 
rows and blocks, but practically no correlation in the case of cent- 
geners. Except for the Lincoln oat, which yielded exceptionally 
high in the nursery, the correlation in the rows and blocks would be 
very high. 

269 * 



56 



EXPERIMENTS IN WHEAT BREEDING. 



Table XXI. — Yields of grain from 11 varieties of oats grown in field plats, centgeners, 

rows, and blocks. 

[The field plats were repeated 3 times, the others 10 times.] 





Average yield of thrashed grain. 


Variety. 


Field 

plats, 

per acre. 


Cent- 

geners. 


Rows. 


Blocks. 




Bushels. 
60.7 
60.6 


Grams. 
729.2 
622.9 


Grams. 
238. 2 
206.9 


Grams. 
1,196.8 




1,047.2 




60.65 


676. 05 


222. 55 


1.122.0 




55.8 
55.3- 
55.2 


584.3 
572.8 
473.7 


213.5 
178.0 
167.0 


865.8 




867.1 




809.8 








54.77 


543.6 


186.16 


847. 56 








51.9 
51.8 
51.0 


550.9 
654.4 
601.3 


170.4 
207. 3 
184.2 


800.8 




1,071.5 




842. 5 








51.56 


602.2 
576.1 


187.3 
177.3 


904. 93 




821.6 








Swedish Select (09) 


50.3 
49.8 
49.3 


560.4 
581.1 
470.3 


170.8 
174.3 
159.6 


791.1 




760. 4 




776.7 








49.83 


537. 26 


168.23 


776. 26 






1 





It is possible that the lack of correlation with the centgeners in 
the last three groups is due to the fact that the lower yielding ones 
were rather late, coarse-strawed, and rank-growing strains. Under 
the thin planting of the centgeners every plant had opportunity to 
develop to full size, which probably gave a slight advantage to the 
later and coarser types, which was not apparent under the usual 
rate of seeding. Table XX, giving results for 24 strains of Turkey 
wheat, shows a perfect correlation between yield of centgener and 
field plats, wherein the wheat strains were all similar, there being no 
great difference in time of maturity or habit of growth. This sug- 
gests that when similar strains are being compared data on the 
average yield of centgeners would be reliable, but that in the case of 
dissimilar varieties, especially of large ones and small ones, the 
results would not be comparable with those obtained under field con- 
ditions. 

COST OF PLANTING AND HARVESTING CENTGENERS, ROWS, AND 

BLOCKS. 

When a large number of strains is being tested in rows or blocks 
and the series is repeated ten to twenty times, the question of time 
and relative cost becomes one of importance. Rapidity of planting 
and harvesting is probably the matter of first consideration, as it is 
desirable to have these operations performed in the shortest possible 
time in order to secure comparable conditions. 

269 



EXPERIMENTAL EKEOR AND VARIATION IN YIELD. 



57 



Table XXII is a summary showing the relative number of plats of 
each kind that can be planted in a day by one gang of men, based on 
our experience. All preliminary work, such as preparing the land, 
sorting and labeling the seed, preparing stakes, etc., is done before- 
hand. However, there is usually time for preliminary work, so that 




Fig. 20.— Five-row nursery drill used for planting row plats and block plats. Four or five men with this 
drill will easily plant 500 row plats in a day, where not more than 100 row plats could be planted by 
hand. The work of the drill is also more uniform and satisfactory than planting by hand. 

the method of planting that permits the greatest rapidity has some 
advantage. The planting is done with a nursery drill (fig. 20), the 
harvesting with hand sickles (fig. 21), and the thrashing with a small 
power machine. 



Table XXII. 



-Comparative number of plats of different types that can be planted or 
harvested in 10 hours. 





Men in 
gang. 


Number of plats covered in 10 hours. 


Kind of plat. 


Planted. 


Harvested. 


Thrashed, 
weighed, 

etc. 


Centgener, using centgener planter 

16-foot row plat, row made with hoe or spade and planted 


5 

5 

5 
5 


100 

100 
500 
150 


250 

500 
500 
200 


500 
750 




750 


Block 4.2 by 16 feet, planted with nursery row drill 


250 



L'G9 



58 



EXPERIMENTS IN WHEAT BREEDING. 



USE OF CHECK PLATS. 

In nursery work where plats are repeated 10 or more times the 
checks will not be needed as a means of correcting error. Their 
principal use here is to determine the degree of experimental error. 
For example, in 1910 we had in one series 80 strains of Turkey 
wheat. The series was repeated 10 times, making 800 rows in all, 
but every fifth row was a check, making 200 check rows. To deter- 
mine the experimental error, the 200 check plats are grouped in sets 
of 10, taking 1 plat from each series, the same as in grouping the 
strains. This method gives 20 sets of 10 checks each, and the range 
of experimental error to be allowed for is at once apparent. 




Fig. 21.— Row plats at harvest time. Each plat is harvested with a hand sickle and the stake tied into 
the bundle. The bundles from the row plats that are to be kept pure for seed should be covered with 
cheese cloth or paper bags. 

Another important use of checks is as a standard by which to 
judge progress, and this judgment can be formed very well if the 
original stock from which selections were made is used for checks. 

Figure 22 illustrates the method of selection when the experimental 
error is determined by the use of checks. Let the figure illustrate an 
ideal case where any number of strains are being compared for yield, 
the yield varying from 200 to 320 pounds. Let line eh represent this 
variation. A series of check plats shows a variation ranging from 
240 to 280, represented by line cj. The mean yield of the checks is 

260 



EXPERIMENTAL ERROR AND VARIATION IN YIELD. 



59 



260, with an extreme error of 20 above or below the mean. The 
limits of error for the line eh are shown by the lines dg and fi. To 
be sure that a certain strain was better than the check plats its yield 
must fall outside the line cl or be better than 280. In the same way 
two strains can not be compared without making an allowance of 40. 
For example, 320 is not surely better than 280, since they both might 
equal 300, but we are sure 320 is better than anything less than 280. 
If the extreme variation of checks should equal the variation in 
strains or varieties, then selection would not be possible. On the 
other hand, if the error in checks is zero, direct comparison between 
strains could be made, and small differences would be significant. 
This illustration emphasizes the importance of knowing the probable 
experimental error and having it well within the limits of expected 
variation if results are to be secured bv selection. 



Y/£LD 

32Q 



240 260 280 300 3ZO 320 

<x b c cC e f 



26Q 



220 




CHfCK PLATS. 



Fig. 22.— Diagram showing the method of selection for yield when the experimental error is known. 



ERROR IN CHECK PLATS. 

By reference to Table XVI it is seen that where odd and even 
numbered (alternate) row plats are checked against each other there 
is a certain experimental error. If this error should be large, it 
would be unsafe to correct by the checks. For example, if the yield 
of a certain check variety equals 100, but in series A its yield, due to 
error, should be 105, and in series B only 95, a correction of yield by 
these checks would introduce an error of 10 per cent. It might hap- 
pen that the strain used for checks would be the most variable strain 

2G9 



60 EXPERIMENTS IN WHEAT BREEDING. 

in use in some particular season, though reliable at other times. For 
this reason care should be taken to ascertain the experimental error 
in checks before using them for correction, else a greater error may 
be introduced by their use than by discarding them. 

OTHER PRECAUTIONS AGAINST ERROR. 
ACCIDENTAL INJURY TO PLATS. 

A problem which always confronts the experimenter at harvest 
time is what to do with plats injured from some cause, such as the 
damage of burrowing animals, being partly washed out by floods, 
etc. Where a plat is obviously injured it should be discarded. To 
allow for accidents we have adopted the plan of planting one or two 
extra series to be discarded or used, as is needful, at harvest time. 
In this way plats accidentally injured may be discarded without dis- 
turbing the regular number in the series. 

UNEQUAL DRAINAGE. 

Unequal effects of winter injury are partly due to unequal distri- 
bution of moisture in the soil. Wherever there is a depression run- 
off water may collect and increase the soil moisture. In some cases, 
as in a very dry spring, these slight depressions may have an advan- 
tage, while at other times these low places suffer from winterkilling. 
Perfect drainage is very important and can be easily secured by lay- 
ing off the nursery in slightly elevated beds about 20 feet in width. 
This bedding can be quickly accomplished by the use of a road grader 
or road drag (PL III, fig.]). 

SUMMARY. 

(1) When 14-foot or 16-foot row plats are used as checks or sown 
in duplicate, great variation is found in yield, owing to natural 
unequal effects of the environment. When the row plats are repeated 
only five or six times, the extreme error will still be large, owing to 
the chance combination of high or low variants. 

(2) Systematic repetition constantly reduces error as the number 
of repetitions increases, but with 16-foot row plats 10 to'20 repetitions 
must be made, depending on the degree of accuracy desired. 

(3) It is probable that the greater the number of strains to be com- 
pared the more repetitions will be necessary, because of the greater 
area they will cover. 

(4) Small blocks, 5.5 feet square, give results similar to those of 
the row plats, except that the reduction of experimental error is some- 
what greater as a result of repetition. Blocks repeated 8 to 10 times 
give results apparently about as accurate as rows repeated 15 to 20 
times. 

209 



EXPERIMENTAL ERROR AND VARIATION IN YIELD. 61 

(5) To increase the size of the block, up to a certain limit, rapidly 
decreases variability; but error can not be indefinitely decreased by 
continuing to increase the size of the plat, as it can be by repetition. 

(6) Variability is not constant from year to year on the same plats. 

(7) To alternate with check rows gives a high degree of accuracy, 
with a few extreme variations, when as high as 10 or more checks are 
used. The total number of plats required for the same degree of 
accuracy, however, is greater by this method than by systematic 
repetition. 

(8) To increase the length of the row 4 times decreases deviation 
about one-half. 

(9) By increasing the length of the row or the size of the block, the 
number of repetitions necessary is decreased, but the total area required 
to secure the same accuracy is increased. An excellent size, where 
land is plenty, would be 2 to 4 rods in length for rows, and 5 by 16 
feet in area for blocks. 

(10) The rate of planting, within certain wide limits, has little influ- 
ence on yield. 

(11) There is some competition between adjacent rows, especially 
when varieties very different in habit of growth are planted side by 
side. The use of blocks does away with this source of error. 

(12) Pure strains differ in a very marked way in most important 
characters. High yield hi the field is associated with high yield hi 
the nursery plats, and strong straw has a slight relation to size of 
plant, no relation to size of berry, and varies inversely with the per- 
centage of nitrogen. 

(13) Block plats and row plats at the usual rates of seeding will 
probably correlate more closely with results infield plats than in plats 
where the plants are spaced, as in centgeners. 

(14) Where error is corrected by the system of repetition of plats, 
check plats should be used for the purpose of determining the experi- 
mental error. When the variation in checks equals the variation in 
strains, no possible selection can be made. 

269 

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